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Rep:Mod:lkb110mod3

2013-02-08T16:44:11Z

Lkb110: /* Conclusion */

==Module 3: Transition States==

In this exercise, gaussian shall be used to calculate transition states, activation energies and conformations to enable comparisons to made between possible reaction paths.

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

[[File:Exo_TS_imag_vib.gif|150px|right|thumb|Imaginary frequency]]

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

===Relative Energies of the Endo/Exo Transition States===

The relative energies are tabulated below.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''
|-
| '''Endo TS''' || -0.05150451 a.u. || 0.68
|-
| '''Exo TS''' || -0.05041985 a.u. || 0.00
|}

From the relative energies it is possible to see that the endo structure is significantly higher in energy that the exo transition state which is not expected. One would expect increased steric repulsion and strain between the axial hydrogen on the cyclo-hexadiene and the bulky oxygens on the malaiec anhydride which does not occur in the endo transition state.

===Comparison of HOMO/LUMO MOs of the Exo/Endo transition states===

[[File:Endo_exo_Mo.png|300px|right]]

The endo conformation is favored in this reaction due to the secondary orbital overlap effect<ref>M.A. Fox, R.Cardona, and N.J.Kiwiet: J.Org.Chem.1987,52,1469-1474</ref>. This occurs where atoms, who are not involved in the bond changing aspect of the reaction, contribute MO overlap in the HOMO transition state. This interaction occurs strongly in the endo TS but not in the exo state, thus providing further stabilization and a preference over the exo transition state. In this specific case secondary orbital overlap comes from the MOs of the (O)C-O-C(O) on the maleic anhydride which, although it is not involved in the bond making/breaking aspect of the reaction, can be seen to interact strongly in the Endo HOMO.

==Conclusion==

Gaussian is a very useful tool which allows the calculation and comparison of transition states, activation energies and conformations. This enables and aids understanding of many complex interactions by visually expressing them through models and animations.

==References==

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T16:43:56Z

Lkb110: /* References */

Rep:Mod:lkb110mod3

2013-02-08T16:43:41Z

Lkb110: /* Comparison of HOMO/LUMO MOs of the Exo/Endo transition states */

==Module 3: Transition States==

In this exercise, gaussian shall be used to calculate transition states, activation energies and conformations to enable comparisons to made between possible reaction paths.

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

[[File:Exo_TS_imag_vib.gif|150px|right|thumb|Imaginary frequency]]

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

===Relative Energies of the Endo/Exo Transition States===

The relative energies are tabulated below.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''
|-
| '''Endo TS''' || -0.05150451 a.u. || 0.68
|-
| '''Exo TS''' || -0.05041985 a.u. || 0.00
|}

From the relative energies it is possible to see that the endo structure is significantly higher in energy that the exo transition state which is not expected. One would expect increased steric repulsion and strain between the axial hydrogen on the cyclo-hexadiene and the bulky oxygens on the malaiec anhydride which does not occur in the endo transition state.

===Comparison of HOMO/LUMO MOs of the Exo/Endo transition states===

[[File:Endo_exo_Mo.png|300px|right]]

The endo conformation is favored in this reaction due to the secondary orbital overlap effect<ref>M.A. Fox, R.Cardona, and N.J.Kiwiet: J.Org.Chem.1987,52,1469-1474</ref>. This occurs where atoms, who are not involved in the bond changing aspect of the reaction, contribute MO overlap in the HOMO transition state. This interaction occurs strongly in the endo TS but not in the exo state, thus providing further stabilization and a preference over the exo transition state. In this specific case secondary orbital overlap comes from the MOs of the (O)C-O-C(O) on the maleic anhydride which, although it is not involved in the bond making/breaking aspect of the reaction, can be seen to interact strongly in the Endo HOMO.

==References==

==Conclusion==

Gaussian is a very useful tool which allows the calculation and comparison of transition states, activation energies and conformations. This enables and aids understanding of many complex interactions by visually expressing them through models and animations.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T16:43:06Z

Lkb110: /* Module 3: Transition States */

Rep:Mod:lkb110mod3

2013-02-08T16:41:15Z

Lkb110: /* Comparison of HOMO/LUMO MOs of the Exo/Endo transition states */

==Module 3: Transition States==

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

[[File:Exo_TS_imag_vib.gif|150px|right|thumb|Imaginary frequency]]

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

===Relative Energies of the Endo/Exo Transition States===

The relative energies are tabulated below.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''
|-
| '''Endo TS''' || -0.05150451 a.u. || 0.68
|-
| '''Exo TS''' || -0.05041985 a.u. || 0.00
|}

From the relative energies it is possible to see that the endo structure is significantly higher in energy that the exo transition state which is not expected. One would expect increased steric repulsion and strain between the axial hydrogen on the cyclo-hexadiene and the bulky oxygens on the malaiec anhydride which does not occur in the endo transition state.

===Comparison of HOMO/LUMO MOs of the Exo/Endo transition states===

[[File:Endo_exo_Mo.png|300px|right]]

The endo conformation is favored in this reaction due to the secondary orbital overlap effect<ref>M.A. Fox, R.Cardona, and N.J.Kiwiet: J.Org.Chem.1987,52,1469-1474</ref>. This occurs where atoms, who are not involved in the bond changing aspect of the reaction, contribute MO overlap in the HOMO transition state. This interaction occurs strongly in the endo TS but not in the exo state, thus providing further stabilization and a preference over the exo transition state. In this specific case secondary orbital overlap comes from the MOs of the (O)C-O-C(O) on the maleic anhydride which, although it is not involved in the bond making/breaking aspect of the reaction, can be seen to interact strongly in the Endo HOMO.

==Conclusion==

Gaussian is a very useful tool which allows the calculation and comparison of transition states, activation energies and conformations. This enables and aids understanding of many complex interactions by visually expressing them through models and animations.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T16:38:40Z

Lkb110: /* Comparison of HOMO/LUMO MOs of the Exo/Endo transition states */

Rep:Mod:lkb110mod3

2013-02-08T16:38:25Z

Lkb110: /* Relative Energies of the Endo/Exo Transition States */

Rep:Mod:lkb110mod3

2013-02-08T16:35:02Z

Lkb110: /* Relative Energies of the Endo/Exo Transition States */

==Module 3: Transition States==

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

[[File:Exo_TS_imag_vib.gif|150px|right|thumb|Imaginary frequency]]

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

===Relative Energies of the Endo/Exo Transition States===

The relative energies are tabulated below.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''
|-
| '''Endo TS''' || -0.05150451 a.u. || 0.68
|-
| '''Exo TS''' || -0.05041985 a.u. || 0.00
|}

From the relative energies it is possible to see that the endo structure is significantly higher in energy that the exo transition state

===Comparison of HOMO/LUMO MOs of the Exo/Endo transition states===

[[File:Endo_exo_Mo.png|300px|right]]

The endo conformation is favored in this reaction due to the secondary orbital overlap effect<ref>M.A. Fox, R.Cardona, and N.J.Kiwiet: J.Org.Chem.1987,52,1469-1474</ref>. This occurs where atoms, who are not involved in the bond changing aspect of the reaction, contribute MO overlap in the HOMO transition state. This interaction occurs strongly in the endo TS but not in the exo state, thus providing further stabilization and a preference over the exo transition state. In this specific case secondary orbital overlap comes from the MOs of the (O)C-O-C(O) on the maleic anhydride which, although it is not involved in the bond making/breaking aspect of the reaction, can be seen to interact strongly in the Endo HUMO.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T16:30:58Z

Lkb110: /* Relative Energies of the Endo/Exo Transition States */

==Module 3: Transition States==

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

[[File:Exo_TS_imag_vib.gif|150px|right|thumb|Imaginary frequency]]

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

===Relative Energies of the Endo/Exo Transition States===

The relative energies are tabulated below.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''
|-
| '''Endo TS''' || -0.05150451 a.u. || 0
|-
| '''Exo TS''' || -234.57119837 a.u. || 0.46
|}

===Comparison of HOMO/LUMO MOs of the Exo/Endo transition states===

[[File:Endo_exo_Mo.png|300px|right]]

The endo conformation is favored in this reaction due to the secondary orbital overlap effect<ref>M.A. Fox, R.Cardona, and N.J.Kiwiet: J.Org.Chem.1987,52,1469-1474</ref>. This occurs where atoms, who are not involved in the bond changing aspect of the reaction, contribute MO overlap in the HOMO transition state. This interaction occurs strongly in the endo TS but not in the exo state, thus providing further stabilization and a preference over the exo transition state. In this specific case secondary orbital overlap comes from the MOs of the (O)C-O-C(O) on the maleic anhydride which, although it is not involved in the bond making/breaking aspect of the reaction, can be seen to interact strongly in the Endo HUMO.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T16:30:30Z

Lkb110: /* Relative Energies of the Endo/Exo Transition States */

==Module 3: Transition States==

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

[[File:Exo_TS_imag_vib.gif|150px|right|thumb|Imaginary frequency]]

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

===Relative Energies of the Endo/Exo Transition States===

The relative energies are tabulated below.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''
|-
| '''Endo TS''' || -234.57046507 a.u. || 0
|-
| '''Exo TS''' || -234.57119837 a.u. || 0.46
|}

===Comparison of HOMO/LUMO MOs of the Exo/Endo transition states===

[[File:Endo_exo_Mo.png|300px|right]]

The endo conformation is favored in this reaction due to the secondary orbital overlap effect<ref>M.A. Fox, R.Cardona, and N.J.Kiwiet: J.Org.Chem.1987,52,1469-1474</ref>. This occurs where atoms, who are not involved in the bond changing aspect of the reaction, contribute MO overlap in the HOMO transition state. This interaction occurs strongly in the endo TS but not in the exo state, thus providing further stabilization and a preference over the exo transition state. In this specific case secondary orbital overlap comes from the MOs of the (O)C-O-C(O) on the maleic anhydride which, although it is not involved in the bond making/breaking aspect of the reaction, can be seen to interact strongly in the Endo HUMO.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T16:28:37Z

Lkb110: /* Comparison of HOMO/LUMO MOs of the Exo/Endo transition states */

==Module 3: Transition States==

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

[[File:Exo_TS_imag_vib.gif|150px|right|thumb|Imaginary frequency]]

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

===Relative Energies of the Endo/Exo Transition States===

===Comparison of HOMO/LUMO MOs of the Exo/Endo transition states===

[[File:Endo_exo_Mo.png|300px|right]]

The endo conformation is favored in this reaction due to the secondary orbital overlap effect<ref>M.A. Fox, R.Cardona, and N.J.Kiwiet: J.Org.Chem.1987,52,1469-1474</ref>. This occurs where atoms, who are not involved in the bond changing aspect of the reaction, contribute MO overlap in the HOMO transition state. This interaction occurs strongly in the endo TS but not in the exo state, thus providing further stabilization and a preference over the exo transition state. In this specific case secondary orbital overlap comes from the MOs of the (O)C-O-C(O) on the maleic anhydride which, although it is not involved in the bond making/breaking aspect of the reaction, can be seen to interact strongly in the Endo HUMO.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T16:28:25Z

Lkb110: /* Comparison of HOMO/LUMO MOs of the Exo/Endo transition states */

==Module 3: Transition States==

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

[[File:Exo_TS_imag_vib.gif|150px|right|thumb|Imaginary frequency]]

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

===Relative Energies of the Endo/Exo Transition States===

==Comparison of HOMO/LUMO MOs of the Exo/Endo transition states==

[[File:Endo_exo_Mo.png|300px|right]]

The endo conformation is favored in this reaction due to the secondary orbital overlap effect<ref>M.A. Fox, R.Cardona, and N.J.Kiwiet: J.Org.Chem.1987,52,1469-1474</ref>. This occurs where atoms, who are not involved in the bond changing aspect of the reaction, contribute MO overlap in the HOMO transition state. This interaction occurs strongly in the endo TS but not in the exo state, thus providing further stabilization and a preference over the exo transition state. In this specific case secondary orbital overlap comes from the MOs of the (O)C-O-C(O) on the maleic anhydride which, although it is not involved in the bond making/breaking aspect of the reaction, can be seen to interact strongly in the Endo HUMO.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T16:26:55Z

Lkb110: /* Comparison of HOMO/LUMO MOs of the Exo/Endo transition states */

==Module 3: Transition States==

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

[[File:Exo_TS_imag_vib.gif|150px|right|thumb|Imaginary frequency]]

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

==Comparison of HOMO/LUMO MOs of the Exo/Endo transition states==

[[File:Endo_exo_Mo.png|300px|right]]

The endo conformation is favored in this reaction due to the secondary orbital overlap effect<ref>M.A. Fox, R.Cardona, and N.J.Kiwiet: J.Org.Chem.1987,52,1469-1474</ref>. This occurs where atoms, who are not involved in the bond changing aspect of the reaction, contribute MO overlap in the HOMO transition state. This interaction occurs strongly in the endo TS but not in the exo state, thus providing further stabilization and a preference over the exo transition state. In this specific case secondary orbital overlap comes from the MOs of the (O)C-O-C(O) on the maleic anhydride which, although it is not involved in the bond making/breaking aspect of the reaction, can be seen to interact strongly in the Endo HUMO.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T16:25:11Z

Lkb110: /* Comparison of HOMO/LUMO MOs of the Exo/Endo transition states */

==Module 3: Transition States==

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

[[File:Exo_TS_imag_vib.gif|150px|right|thumb|Imaginary frequency]]

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

==Comparison of HOMO/LUMO MOs of the Exo/Endo transition states==

[[File:Endo_exo_Mo.png|300px|right]]

The endo conformation is favored in this reaction due to the secondary orbital overlap effect<ref>M.A. Fox, R.Cardona, and N.J.Kiwiet: J.Org.Chem.1987,52,1469-1474</ref>. This occurs where atoms, who are not involved in the bond changing aspect of the reaction, contribute MO overlap in the HOMO transition state. This interaction occurs strongly in the endo TS but not in the exo state, thus providing further stabilization and a preference over the exo transition state. In this specific case secondary orbital overlap comes from the MOs of the (O)C-O-C(O) on the malae

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T16:23:29Z

Lkb110: /* Comparison of HOMO/LUMO MOs of the Exo/Endo transition states */

==Module 3: Transition States==

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

[[File:Exo_TS_imag_vib.gif|150px|right|thumb|Imaginary frequency]]

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

==Comparison of HOMO/LUMO MOs of the Exo/Endo transition states==

[[File:Endo_exo_Mo.png|300px|right]]

The endo conformation is favored in this reaction due to the secondary orbital overlap effect<ref>M.A. Fox, R.Cardona, and N.J.Kiwiet: J.Org.Chem.1987,52,1469-1474</ref>. This occurs where atoms, who are not involved in the bond changing aspect of the reaction, contribute MO overlap in the HOMO transition state. This interaction occurs strongly in the endo TS but not in the exo state, thus providing further stabilization and a preference over the exo transition state.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T16:16:43Z

Lkb110: /* Module 3: Transition States */

==Module 3: Transition States==

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

[[File:Exo_TS_imag_vib.gif|150px|right|thumb|Imaginary frequency]]

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

==Comparison of HOMO/LUMO MOs of the Exo/Endo transition states==

[[File:Endo_exo_Mo.png|300px|right]]

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T16:13:51Z

Lkb110: /* Comparison of HOMO/LUMO MOs of the Exo/Endo transition states */

==Module 3: Transition States==

Transition states are defined as ...........................................

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

[[File:Exo_TS_imag_vib.gif|150px|right|thumb|Imaginary frequency]]

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

==Comparison of HOMO/LUMO MOs of the Exo/Endo transition states==

[[File:Endo_exo_Mo.png|300px|right]]

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T16:13:28Z

Lkb110: /* Comparison of HOMO/LUMO MOs of the Exo/Endo transition states */

File:Endo exo Mo.png

2013-02-08T16:13:06Z

Lkb110:

Rep:Mod:lkb110mod3

2013-02-08T16:05:11Z

Lkb110: /* Intrinsic Reaction Coordinate of Endo-Transition state */

Rep:Mod:lkb110mod3

2013-02-08T15:36:39Z

Lkb110: /* Optimisation of Exo-Transition state */

Rep:Mod:lkb110mod3

2013-02-08T15:35:52Z

Lkb110: /* Optimisation of Exo-Transition state */

==Module 3: Transition States==

Transition states are defined as ...........................................

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

[[File:Exo_TS_imag_vib.gif|250px|right|thumb|Imaginary frequency]]

An imaginary frequency is present at -812.2483 cm^-1 (animation displayed to the right) indicates the transition state has been reached and the synchronous bond formation.

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T15:33:23Z

Lkb110: /* Optimisation of maleic anhydride using "Semi-Empirical/AM1" method */

==Module 3: Transition States==

Transition states are defined as ...........................................

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

Therefore an imaginary frequency is present at -812.2483 cm^-1, an animation of said frequency is shown below.

[[File:Exo_TS_imag_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T15:32:54Z

Lkb110: /* Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method */

==Module 3: Transition States==

Transition states are defined as ...........................................

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence was achieved and the molecule optimised.

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

Therefore an imaginary frequency is present at -812.2483 cm^-1, an animation of said frequency is shown below.

[[File:Exo_TS_imag_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T15:32:14Z

Lkb110: /* Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition */

==Module 3: Transition States==

Transition states are defined as ...........................................

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

The Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride has two possible routes and products, endo and exo, depending on which orientation maleic anhydride adopts when approaching Cyclohexa-1,3-diene.

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

Therefore an imaginary frequency is present at -812.2483 cm^-1, an animation of said frequency is shown below.

[[File:Exo_TS_imag_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T15:24:04Z

Lkb110: /* Cyclohexa-1,3-diene and maleic anhydride: Diels-Alder Cycloaddition */

==Module 3: Transition States==

Transition states are defined as ...........................................

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Regioselectivity of Diels-Alder Cycloaddition==

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

Therefore an imaginary frequency is present at -812.2483 cm^-1, an animation of said frequency is shown below.

[[File:Exo_TS_imag_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T15:21:51Z

Lkb110: /* Intrinsic Reaction Coordinate */

==Module 3: Transition States==

Transition states are defined as ...........................................

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below is the animation of the IRC calculation. It shows the ethylene approaching the cis-butadiene from above the plane of the molecule leading to maximum overlap of the appropriate orbitals shown in the FMO diagram below.

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|500px|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Diels-Alder Cycloaddition==

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

Therefore an imaginary frequency is present at -812.2483 cm^-1, an animation of said frequency is shown below.

[[File:Exo_TS_imag_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T15:19:53Z

Lkb110: /* Intrinsic Reaction Coordinate */

==Module 3: Transition States==

Transition states are defined as ...........................................

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

[[File:IRC_graph_cisbut.svg|500px|right|thumb| IRC reaction coordinate]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Diels-Alder Cycloaddition==

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

Therefore an imaginary frequency is present at -812.2483 cm^-1, an animation of said frequency is shown below.

[[File:Exo_TS_imag_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T15:18:16Z

Lkb110: /* Intrinsic Reaction Coordinate */

==Module 3: Transition States==

Transition states are defined as ...........................................

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_cisbut.svg|500px|centre]]

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|centre|thumb|Frontier MOs of cisbutadiene and ethylene]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Diels-Alder Cycloaddition==

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

Therefore an imaginary frequency is present at -812.2483 cm^-1, an animation of said frequency is shown below.

[[File:Exo_TS_imag_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T15:16:11Z

Lkb110: /* Optimisation of Cis-butadiene/ethylene transition state */

==Module 3: Transition States==

Transition states are defined as ...........................................

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right) this vibration displaces the position of the terminal carbon atoms hindering the bond formation.

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_cisbut.svg|500px|centre]]

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|centre]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Diels-Alder Cycloaddition==

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

Therefore an imaginary frequency is present at -812.2483 cm^-1, an animation of said frequency is shown below.

[[File:Exo_TS_imag_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

<references>

</references>

Rep:Mod:lkb110mod3

2013-02-08T15:12:24Z

Lkb110: /* Optimisation of Cis-butadiene/ethylene transition state */

==Module 3: Transition States==

Transition states are defined as ...........................................

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

The transition state has been reached therefore an imaginary frequency is present at -951.8029 cm^-1, An animation of this frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]
[[File:Lowest_positive_vibration.gif|150px|right|thumb|Lowest positive frequency (147.99cm^-1)]]

From this animation is can be deduced that the bond formation is synchronous. However when compared to the lowest positive vibrational frequency (shown to the right)

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_cisbut.svg|500px|centre]]

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|centre]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Diels-Alder Cycloaddition==

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

Therefore an imaginary frequency is present at -812.2483 cm^-1, an animation of said frequency is shown below.

[[File:Exo_TS_imag_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

<references>

</references>

File:Lowest positive vibration.gif

2013-02-08T15:11:09Z

Lkb110:

Rep:Mod:lkb110mod3

2013-02-08T15:02:33Z

Lkb110: /* Optimisation of Cis-butadiene/ethylene transition state */

==Module 3: Transition States==

Transition states are defined as ...........................................

== The Cope Rearrangement of 1,5-hexadiene==

[[File:Cope_rearrangement_pic.png|250px|right|thumb| Cope Rearrangement Mechanism]]
[[File:Gauche_app_newman_projection.png|right|thumb| Gauch and Anti-periplanarNewman projections]]

The Cope Rearrangement, shown to the right <ref> H. Rzepa, Pericyclic Reactions, 2nd year Imperial College London lecture course, 2012 </ref> , is classified as an intramolecular 3,3 sigmatropic rearrangement which can adopt either the "chair" or "boat" conformation. Activated by heat and corresponding to a 4n+2 Π system, the reaction occurs through a concerted mechanism via a Huckel transition state.

1,5-hexadiene can adopt ten different low energy conformations both in the gauche and anti-periplanar form. In the gauche conformation the largest groups, in the case the double bonds are arranged at 60 degrees to one another when viewed along the C3-C4 bond. Whereas in anti-periplanar conformers the largest groups are situated at 180 degrees from on another when viewed in the same way. This can be seen more clearly from the newman projections to the right of this page.

To assertain which are of the lowest energy, the structures were drawn on GaussView 5.0 and optimised using the "Hartree-Fock" method and the 3-21G basis set.

The calculation output is tabulated below:

{| class="wikitable" border="1"
|+
! '''Conformer''' !! '''Structure''' !! '''Point Group''' !! ''' Energy (HF/3-21G)''' !! '''Relative Energy (kcal/mol)''' !! ''' Calculation output .log file'''
|-
| '''''Gauche1''''' || [[File:Gauch1_pic.png|150px]] || C2 || -231.68771613 a.u. ||3.10 || [[Media:GAUCHE1_OPT_321G_MON.LOG]]
|-
| '''''Gauche2''''' || [[File:Gauche2_pic.png|150px]] || C2 || -231.69166701 a.u. ||0.62 ||[[Media:GAUCHE_OPT1_321G.LOG]]
|-
| '''''Gauche3''''' || [[File:Gauche3_pic.png|150px]] || C1 || -231.69266120 a.u. ||0 || [[Media:GAUCHE1_OPT_321G.LOG]]
|-
| '''''Gauche4''''' || [[File:Gauche4_pic.png|150px]] || C2 || -231.69153036 a.u. ||0.71 || [[Media:REACT_GAUCHE_OPT_321G.LOG‎]]
|-
| '''''Gauche5''''' || [[File:Gauche5_pic.png|150px]] || C1 || -231.68961573 ||1.91 || [[Media:GAUCHE5_OPT_321G_MON.LOG‎]]
|-
| '''''Gauche6''''' || [[File:Gauche6_pic.png|150px]] || C1 || -231.68916016 a.u. ||2.20 || [[Media:GAUCHE6_OPT_321G_MON.LOG]]
|-
| '''''Anti1''''' || [[File:Anti1_pic.png|150px]] || C2|| -231.69260236 a.u.||0.04 || [[Media:ANTI_OPT2_321G.LOG]]
|-
| '''''Anti2''''' || [[File:Anti2_pic.png|150px]] || Ci|| -231.69253530 a.u.|| 0.08 || [[Media:‎REACT ANTI OPT 321G.LOG]]
|-
| '''''Anti3''''' || [[File:Anti3_pic.png|150px]] || C2h || -231.68907066 a.u. ||2.25|| [[Media:ANTI3_OPT_321G_MON.LOG]]
|-
|'''''Anti4''''' || [[File:Anti4_pic.png|150px]] || C1 || -231.69097054 a.u. ||1.06 || [[Media:ANTI_OPT4_321G.LOG]]
|}

[[File:Gauche3_anti1_2_newmans.png|right|thumb| Gauche1, Anti1 and Anti2 Newman projections]]

The relative energies were calculated and it can therefore be deduced that ''Gauche3'',''Anti1'' and ''Anti2'' are the lowest energy conformers of 1,5-hexadiene. From the table it can be seen that conformers Anti1 and Anti2 are slightly more destabilised than Gauche3 in the order gauche3>anti1>anti2 where gauche3 is the most stable. The gauche conformation is generally assumed to be the least stable due to the proximity of the larger substituents in the molecule and increased posibility of steric repulsion. However, in this case, gauche3 is the most stable. In this calculation a low basis set has been used which may explain these unexpected results. Therefore Gauche3, Anti1 and Anti2 will be further optimised using a higher level of theory, DFT/B3LYP/6-31G*, to give a more accurate overview of the structures.

===Optimisation and Frequency Analysis of Gauche3 conformer 1,5-hexadiene using the DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of gauche3 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:GAUCHE3_OPT_FREQ%2B631G.LOG]].

[[File:Gauch3_631g_pic.png|250px|right|thumb|Optimised structure of gauche3 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||GAUCHE3_opt_freq+631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57046507 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000600 a.u.
|-
|'''Dipole Moment''' || 0.4830 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 7 minute 4.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000868 0.001800 YES
RMS Displacement 0.000205 0.001200 YES
Predicted change in Energy=-3.742255D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -10.2189 -6.4944 -0.0008 -0.0004 0.0008 7.6458
Low frequencies --- 71.3146 97.7578 120.8349
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti1'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the optimised structure of Anti1 1,5-hexadiene calculated earlier, the structure was further optimised using a higher level of theory and frequency analysis was done. The calculation was run through gaussian and the output linked here: [[Media:ANTI1_OPT_FREQ_631G.LOG]].

[[File:Anti1 631G pic.png |250px|right|thumb|Optimised structure of anti1 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' ||anti_opt_freq_631g
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57119837 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00003290 a.u.
|-
|'''Dipole Moment''' || 0.2902 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 6 minute 49.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000046 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000527 0.001800 YES
RMS Displacement 0.000175 0.001200 YES
Predicted change in Energy=-5.051719D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -20.8055 -8.8434 -0.0011 -0.0007 -0.0007 10.0109
Low frequencies --- 72.3096 100.1289 107.3776
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Optimisation and Frequency Analysis of ''Anti2'' 1,5-hexadiene conformer using DFT/B3LYP/6-31G* level of theory===

Using the previously optimised Anti2 conformer, the molecule was further optimised using a higher level of theory and frequency analysis was conducted using job type "opt+freq", method "DFT/B3LYP" and basis set 6-31G*. The calculation was run through gaussian and the output linked here: [[Media: REACT_ANTI_OPT_FREQ_621G.LOG‎]]

[[File:Anti2_631G_pic.png |250px|right|thumb|Optimised structure of anti2 conformer]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || REACT_GAUCHE_OPT_FREQ_621G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.57111273 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000118 a.u.
|-
|'''Dipole Moment''' || 0.000 Debye
|-
|'''Point Group''' || Ci
|-
|'''Calculation Time''' || 10 minute 34.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000053 0.000060 YES
RMS Displacement 0.000020 0.000040 YES
Predicted change in Energy=-9.670423D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -7.2270 -2.6795 -0.0010 -0.0008 -0.0007 1.8403
Low frequencies --- 71.6151 78.8116 116.4168
</pre>

These extracts show that convergence has been achieved and a minimum met. The molecule has been successfully optimised.

===Comparison of Low Energy Structures using a higher level of theory===

Having optimised the three lowest energy conformers of 1,5-hexadiene using the DFT/B3LYP/6-31G* method, the relative energies were calculated.

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !!'''Total Energy'''''!! '''Relative Energy (kcal/mol)'''!! '''Experimental Relative Energy (kcal/mol) <ref>B. W. Gung, Z. Zhu and R. A. Fouch, J. Am. Chem. Soc., 1995, 117, 1783-1788.</ref>'''
|-
| '''Gauche3''' || -234.57046507 a.u. || 0 || 0.34
|-
| ''' Anti1 ''' || -234.57119837 a.u. || 0.46 || 0.05
|-
| '''Anti2''' || -234.57111273 a.u. || 0.41 || 0.00
|}

The above table shows that, according to experimental data, Anti1 is the lowest energy conformer. However, according to the calculations run through gaussian, gauche3 remains the lowest energy confromation. This suggests an error in the calculation of the gauche3 structure as the difference between the relative energies of anti1 and anti2 correspond to the 0.05kcal/mol difference seen from the experimental relative energies. Despite numerous attempts, I have not been able to rectify the problem with the gauche3 optimisation within the time given.

{| class="wikitable" border="1"
|+
|-
! '''Bond Length''' !!'''Hartree Fock/3-21G ''Gauche3'''''!! '''DFT/B3LYP/6-31G* ''Gauche3'''''!! '''Hartree Fock/3-21G ''Anti1'''''!!'''DFT/B3LYP/6-31G* ''Anti1'''''!! '''Hartree Fock/3-21G ''Anti2'''''!! '''DFT/B3LYP/6-31G* ''Anti2'''''
|-
| '''C2-C3/C4-C5 (Å)''' ||1.50847||1.50860||1.50884 ||1.50769 ||1.50889 || 1.50778
|-
| ''' C3-C4 '''(Å) || 1.55323||1.55687||1.55237||1.55434||1.55291 ||1.55499
|-
| '''C=C'''(Å) ||1.31631||1.34147||1.31610||1.34147|| 1.31615 ||1.34145
|-
| ''' Dihedral Angle'''(degrees) ||67.969|| 66.973||176.912||175.818|| 180 ||180
|}

When comparing the geometries of the structures (tabulated above) the higher level calculation has not made any drastic alterations to the structure of the molecule. However these small changes in bond length and dihedral angle will ultimately change to the total energy of the molecule. No imaginary frequencies were observed for any of the optimisations showing them to be successful

===Thermochemistry of 1,5-hexadiene with DFT/B3LYP/6-31G* level of theory===

{| class="wikitable" border="1"
|+
|-
! '''Conformer''' !! '''Sum of Electronic and Zero Point Energy (Hartree)'''!! '''Sum of electronic and thermal energy(Hartree)''' !! '''Sum of electronic and thermal enthalpy(Hartree)''' !! '''Sum of electronic and thermal free energy(Hartree)'''
|-
|'''''Anti1'''''|| -234.428156 || -234.420873 || -234.419929 || -234.459746
|-
| '''''Anti2''''' || -234.428074 || -234.420768 || -234.419824 || -234.459702
|-
| '''''Gauche3''''' || -234.427302 || -234.420105 || -234.419161 || -234.458800
|}

The optimisation of these structures at the DFT/B3LYP/6-31G* level also calculated the Energies displayed in the table above.

[[File:Cope_diagram.png|300px|left|thumb|Cope Rearrangement<ref> B. W.Gung,Z.Zhu,R.A.Fouch: J. Org. Chem. 2003, 68, 572-577 </ref>]]

=="Chair" Transition State==

The Cope Rearrangement reaction can run via two possible transition states; the "chair" and the "boat" , shown in the figure to the left. Gaussian enables the calculation of the transition state structures.

[[File:Allyl_fragment_pic.png|100px|right|thumb|Optimised Allyl fragment]]

===Optimisation of the allyl structure===

An allyl fragment was drawn on gaussian and optimised using the "Hartree-Fock" method and "3-21G" basis set. The output of the calculation is linked here: [[Media:ALLYL_OPT_HF_321G.LOG]]

The optimised is shown to the right of this page and a summary of the calculation is tabulated below.

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || ALLYL_OPT_HF_321G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || UHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Doublet
|-
| ''' Total Energy''' || -115.82303991 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00009674 a.u.
|-
|'''Dipole Moment''' || 0.0293 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000160 0.000450 YES
RMS Force 0.000056 0.000300 YES
Maximum Displacement 0.000711 0.001800 YES
RMS Displacement 0.000290 0.001200 YES
Predicted change in Energy=-1.860815D-07
Optimization completed.
-- Stationary point found.
</pre>

Convergence has been achieved.

===Optimisation of Guess "Chair" Transition State using the Hartree Fock/3-21G level of theory===

[[File:Chair_ts_pic_1.png|right|thumb|Screen shots of optimised "chair" transition state|150px]]

Two optimised allyl structures from the previous calculation were superimposed, with the terminal carbons spaced ~2.2 Å apart, to guess the "chair" transition state structure. An optimisation calculation was then run on the structure using method "opt +freq", optimising to a transition state (Berny). Additional keywords used were "Opt=NoEigen". The ouput of the calculation is linked here: [[Media:CHAIR_TS_GUESS.LOG]].

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002546 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 14.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000845 0.001800 YES
RMS Displacement 0.000103 0.001200 YES
Predicted change in Energy=-4.366750D-08
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vibration.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:
<pre>
Low frequencies --- -818.0217 -0.0004 -0.0001 0.0007 2.9124 2.9923
Low frequencies --- 5.0173 209.6099 395.9575
</pre>

The imaginary frequency at -818.0217 cm^-1 represents the maxima has been obtained on the potential energy curve and thus the transition state.

===Further Optimisation of "Chair" Transition State using the Frozen coordinate method===

The "Chair" transition state was further optimised using the frozen coordinate methods, where the distances between the terminal carbon atoms of the 2 allyl groups were frozen at 2.2 Å during the optimisation using the "Redundant Coord Editor". Calculation methods identical to those used for the optimisation of the "guess" chair TS were utilised for this for this calculation. i.e. the structure was optimised to "TS (berny)".

The output of this calculation is linked here: [[Media:CHAIR_TS_FREEZE_COORD_3.LOG‎]]

A summary of the calculation is tabulated below.

[[File:Frozen_coordinate_chair_pic.png|150px|right|thumb|Chair Transition state optimised using Frozen coordinate method]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_FREEZE_COORD_3
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932243 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002549 a.u.
|-
|'''Dipole Moment''' || 0.0008 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000072 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000420 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-3.637521D-08
Optimization completed.
-- Stationary point found.
</pre>

===Final Optimisation of "Chair" Transition State using the normal guess hessian===

The removal of the frozen coordinates allows the distance itself to be optimised during this final calculation by introducing normal guess hessian. This is achieved by selecting "derivative" in the Redundant Coordinate Editor instead of "Frozen coordinate".

The output of this calculation is linked here: [[Media:CHAIR_TS_DERIVATIVE_MONDAY.LOG]]

[[File:Final_chair_pic.png|250px|right|thumb|Optimised Chair Transition State]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_DERIVATIVE_MONDAY
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FTS
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.61932238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00007028 a.u.
|-
|'''Dipole Moment''' || 0.0010 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.000464 0.001800 YES
RMS Displacement 0.000082 0.001200 YES
Predicted change in Energy=-2.165121D-08
Optimization completed.
-- Stationary point found.
</pre>

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.01941 Å
|-
| '''Internal C-C (on allyl)''' || 1.38939 Å
|-
| '''Internal C-C-C angle''' || 120.496 degrees
|}

===Intrinsic Reaction Coordinate===

This method allows the product structure to be found by following the minimum energy pathway down to the minimum on the Potential energy surface. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:CHAIR_TS_IRC_2.LOG]]

[[File:IRC_structure_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_IRC_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69157975 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00015222 a.u.
|-
|'''Dipole Moment''' || 0.3632 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 5 minutes 36.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graphs.svg|500px|center]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. Therefore, the final structure from the IRC calculation will be minimised to reach the true minimum. Each point on the graph corresponds to the movement in the animation below.

[[File:Chair_IRC_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Minimised_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || Chair_IRC_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69166702 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000804 a.u.
|-
|'''Dipole Moment''' || 0.3804 Debye
|-
|'''Point Group''' || C2
|-
|'''Calculation Time''' || 10.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001402 0.001800 YES
RMS Displacement 0.000452 0.001200 YES
Predicted change in Energy=-7.532587D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -2.0842 -1.5920 -0.0008 -0.0008 -0.0008 0.9690
Low frequencies --- 63.6702 98.1812 113.3898
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche2'''''.

===Optimisation of "Chair" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated chair transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_TS_OPT_FREQ_631G.LOG]]

[[File:631G_chair_ts.png|200px|right|thumb|DFT/B3LYP/6-31G* optimised chair TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CHAIR_TS_opt_freq_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.51595692 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001471 a.u.
|-
|'''Dipole Moment''' || 0.0000 Debye
|-
|'''Point Group''' || C2h
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000039 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000837 0.001800 YES
RMS Displacement 0.000214 0.001200 YES
Predicted change in Energy=-5.243525D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -555.7364 -0.0008 -0.0007 -0.0004 18.3528 20.8306
Low frequencies --- 36.3822 189.6868 240.2280
</pre>

Again, the presence of a negative, imaginary frequency indicates the transition state has been reached.

The geometries of the optimised chair transition state are tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.05553 Å
|-
| '''Internal C-C (on allyl)''' || 1.40796 Å
|-
| '''Internal C-C-C angle''' || 121.251 degrees
|}

=="Boat" Transition State==

===Optimisation of the "Boat" Transition State===

A different method is used to calculate the transition state of the "boat" conformation. In this case the "QST2" method will be used. The optimised ''Anti2'' conformation of 1,5-hexadiene with Ci symmetry(optimised in an earlier section) was taken and the numbered so that the movement of the atoms could be monitored before and after the 3,3 sigmatropic rearrangement.

[[File:Boat_numbered_anti2.png|300px|centre|thumb|Labelled 1,5-hexadiene (Reactant to the left, product to the right)]]

The calculation was run through gaussian using Job type "opt + freq", optimising to "TS (QST2)", the method used was "Hartree-Fock" and Basis set "3-21G".

However, this calculation failed due to the vast difference between the reactant/product structures and the transition state and gaussian not recognising the need for rotation around the C-C bond.

Therefore, the by altering the dihedral angles (C2-C3-C4-C5) on the reactant/product structures to 0 degrees and the angles C2-C3-C4/C3-C4-C5 to 100 degrees and re-running the calculation (making sure the numbering exactly matches that of the diagram below, otherwise the calculation is unsuccessful).

[[File:Numbered_reactant_product_pic.png|350px|centre|thumb|Numbered anti-periplanar 1,5-hexadiene]]

The calculation is successful and the output is linked here: [[Media:OPT_BOAT_QST2_321G_2.LOG]].

A summary of the calculation is tabulated below.

[[File:Combo_boat_ts_pic.png|150px|right|thumb|Optimised Boat Transition state]]

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || OPT_BOAT_QST2_321G_2
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002948 a.u.
|-
|'''Dipole Moment''' || 0.1583 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 8.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000045 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.001318 0.001800 YES
RMS Displacement 0.000349 0.001200 YES
Predicted change in Energy=-1.056572D-07
Optimization completed.
-- Stationary point found.
</pre>
[[File:Imaginary_vib_animation.gif|150px|right|thumb|Imaginary frequency]]

Frequency analysis shows the presence of an imaginary vibration, shown below:

<pre>
Low frequencies --- -840.0322 -3.2450 -1.0360 -0.0005 -0.0004 0.0002
Low frequencies --- 3.0197 155.2630 382.0773
</pre>

Animation of imaginary vibration reported at frequency -840.0322 cm^-1 indicates the transition state has been reached.

===Intrinsic Reaction Coordinate===

As with the chair transition state, the IRC is used to calculate the product structure of the cope rearrangement. This is achieved by taking the optimised transition state and running a calculation on it. The job type used was "IRC", parameters were set to compute the forward reaction only (due to the symmetric nature of the reaction), to calculated the force constant "always" at each point along the IRC and to compute 50 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:BOAT_IRC.LOG]]

[[File:Boat_IRC_pic.png|250px|right|thumb|Final IRC Calculation structure]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || BOAT_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.60280238 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002946 a.u.
|-
|'''Dipole Moment''' || 1583 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 6 minutes 48.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_pathway_graph.svg|500px|centre]]

This shows the IRC to be approaching a minimum, however the RMS gradient is still relatively large suggesting it has yet to be reached. The below animation corresponds to the IRC graph.

[[File:Boat_irc_movie.gif|centre]]

An "opt+freq" calculation was conducted using the "Hartree-Fock" method and the "3-21G" basis set to reach the true minimum. The calculation was run through gaussian and the output linked here: [[Media:CHAIR_IRC_MINIMISE.LOG]].

[[File:Boat_minimise_pic.png|250px|right|thumb|Minimised IRC Structure]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_irc_minimise
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RHF
|-
| '''Basis Set''' || 3-21G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -231.69266120 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000496 a.u.
|-
|'''Dipole Moment''' || 0.3406 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 9.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000010 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001762 0.001800 YES
RMS Displacement 0.000466 0.001200 YES
Predicted change in Energy=-1.371128D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -1.9359 -0.0144 -0.0005 -0.0003 0.0005 2.0646
Low frequencies --- 74.5844 104.9906 130.5564
</pre>

By comparison of the structure and its total energy to the conformers of 1,5-hexadiene in the table a t the top of this wikipage. It can be deduced that the product of the cope rearrangement passing through the "chair" transition state is '''''Gauche3'''''.

===Optimisation of "Boat" Transition State using the DFT/B3LYP/6-31G* method===

The starting molecule for this calculation was the optimisated boat transition state using the "Hartree-Fock" method and "3-21G" basis set. The calculation was set up using "opt+freq" job type, optimising to "TS (Berny)" with the force constant being calculated once. The method used was DFT/B3LYP/6-31G*. The calculation was run through gaussian and the output linked here: [[Media:BOAT_TS_OPT_631G.LOG]]

[[File:631G_boat_pic.png|200px|right|thumb|DFT/B3LYP/6-31G* Optimised Boat TS]]

A summary of the calculation is tabulated below:

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || boat_ts_opt_631G
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RB3LYP
|-
| '''Basis Set''' || 6-31+G
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -234.50425982 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000807 a.u.
|-
|'''Dipole Moment''' || 0.0123 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 4 minutes 15.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000405 0.001800 YES
RMS Displacement 0.000104 0.001200 YES
Predicted change in Energy=-1.682190D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -475.9916 -16.5061 -0.0003 0.0003 0.0011 10.9975
Low frequencies --- 19.3829 133.3606 247.4065
</pre>

Imaginary frequency has been found signifying the transition state has been reached.

The geometries of the optimised boat transition state is tabulated below.
{| class="wikitable" border="1"
|+
|-
| '''Terminal C- Terminal C''' || 2.29118 Å
|-
| '''Internal C-C (on allyl)''' || 1.39617 Å
|-
| '''Internal C-C-C angle''' || 123.158 degrees
|}

==Activation Energy of the "boat" and "chair" transition states==

The activation energies of the two reaction paths were calculated by subtracting the energy of the starting material, in this case the Anti2 conformation of 1,5-hexadiene, from the energy of the transition states.

The results are tabulated below:

{| class="wikitable" border="1"
|+
|-
! !!'''Electronic energy (HF/3-21G)'''''!! '''Sum of electronic and zero-point energies'''(HF/3-21G)!! '''Sum of electronic and thermal energies'''(HF/3-21G) !! '''Electronic energy'''(B3LYP/6-31G*)!!'''Sum of electronic and zero-point energies'''(B3LYP/6-31G*)!!'''Sum of electronic and thermal energies(B3LYP/6-31G*)'''
|-
| || || '''at 0K'''|| '''at 298.15K|| || '''at 0K'''|| '''at 298.15K'''
|-
| '''Chair TS''' || -231.61932238 a.u || -231.466702 a.u. || -231.461342 a.u.||-234.51595692 a.u. || -234.373713 a.u.|| -234.367725 a.u.
|-
| '''Boat TS''' ||-231.60280238 a.u || -231.450928 a.u. || -231.445299a.u. || -234.50425982 a.u.|| -234.363284 a.u. || -234.356891 a.u.
|-
| '''Reactant (Anti2)''' ||-231.69253530 a.u ||-231.539540 a.u.||-231.532566 a.u.||-234.57111273 a.u || -234.428074 a.u.|| -234.420768 a.u.
|}

{| class="wikitable" border="1"
|+
|-
! !!'''HF/3-21G'''!! '''HF/3-21G'''!! '''B3LYP/6-31G*'''!!'''B3LYP/6-31G*'''!! '''Experimental''' <ref>M. Bearpark, https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:phys3.</ref>
|-
| || at 0k || at 298.15K || at 0K || at 298.15K || at 0K
|-
| '''ΔE (Chair)''' (kcal/mol)|| 41.33 || 44.69|| 34.11 || 33.28 || 33.5 ± 0.5
|-
| '''ΔE (Boat) '''(kcal/mol) || 55.60 || 54.76 || 40.66 || 40.08 || 44.7 ± 2.0
|}

From these activation energies it can be deduced that the "chair" transition state has the lowest activation energy and therefore the lowest energy route to the products.

==Cis Butadiene and Ethylene: Diels Alder Cycloaddition==

[[File:Cisbutadiene_ethylene_chemdraw.png|150px|right|thumb|Cis Butadiene + Ethylene]]

===Optimisation of Cis Butadiene===

Cis-butadiene was built on gaussian and optimised using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media:CISBUTADIENE_OPT_SE_AM1.LOG]].

[[File:HOMO_LUMO_MOS_CIS_BUT.png|300px|right|thumb|Optimised Cis-butadiene HOMO and LUMO]]
[[File:HOMO_LUMO_chem_draw_cis_but.png|300px|right|thumb| Cis-butadiene HOMO and LUMO MOs]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CISBUTADIENE_OPT_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.04879734 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00008900 a.u.
|-
|'''Dipole Moment''' || 0.0414 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000159 0.000450 YES
RMS Force 0.000051 0.000300 YES
Maximum Displacement 0.000768 0.001800 YES
RMS Displacement 0.000254 0.001200 YES
Predicted change in Energy=-1.540730D-07
Optimization completed.
-- Stationary point found.
</pre>

Therefore it can be seen that the HOMO of cis-butadiene is asymmetric with respect to the plane whilst the LUMO is symmetric.

===Optimisation of Cis-butadiene/ethylene transition state===

[[File:Guess_TS_input.png|250px|right|thumb|Guess input structure of cis-butadiene/ethylene transition state]]

A guess structure of the transition state between cis-butadiene and ethylene was built on gaussian, shown to the right.
This structure was then optimised to a transition state using the "opt +freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:DIELS_ALDER_TS_OPT_GUESS.LOG]]

[[File:TS_HOMO_LUMO_MO.png|300px|right|thumb|Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]
[[File:TS_HOMO_LUMO_chemdraw.png|300px|right|thumb| Optimised Cis-butadiene/Ethylene TS: HOMO and LUMO]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000751 0.001800 YES
RMS Displacement 0.000231 0.001200 YES
Predicted change in Energy=-1.254035D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -951.8029 -13.3745 -8.7621 -5.1549 0.0024 0.0433
Low frequencies --- 0.0789 147.9895 244.8410
</pre>

Therefore an imaginary frequency is present at -951.8029 cm^-1, an animation of said frequency is shown below.

[[File:Guess_imaginary_freq_animation.gif|250px|centre]]

The geometries of the transition state are tabulated below.

{| class="wikitable" border="1"
|+
|-
| Partially formed C=C || 1.39777Å
|-
| Partially formed C-C || 2.11807Å
|}

Stated here are literature values of sp3 C-C(1.330Å) and sp2 C=C (1.443Å)<ref>F. H. Allen, O. kennard and D. G. Watson, J. Chem. Soc. Perkin Trans., 1987, II, S7-S8.</ref> These are longer than the calculated lengths recorded above which makes sense as the calculated bond lengths have yet to fully form. The van der waals radius of a carbon atom is 1.7Å <ref> A.Bondi: J. Phys. Chem., 1964, 68 (3), pp 441–451 </ref>. The partially formed C-C bond is outside of this range showing the molecules need to move into position before the van der waals can have some effect.

===Intrinsic Reaction Coordinate===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:DIELS_ALDER_IRC.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_IRC
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || 0.07462541 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005683 a.u.
|-
|'''Dipole Moment''' || 0.0374 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 2 minutes 57.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_cisbut.svg|500px|centre]]

[[File:Cis_but_TS_movie.gif|centre]]

[[File:Orbital_diagram.png|centre]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: DIELS_ALDER_IRC_MINIMISE.LOG]]

[[File:Minimised_product.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || DIELS_ALDER_TS_OPT_GUESS
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.11033724 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000955 a.u.
|-
|'''Dipole Moment''' || 0.8379 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 18.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000056 0.000450 YES
RMS Force 0.000013 0.000300 YES
Maximum Displacement 0.000642 0.001800 YES
RMS Displacement 0.000164 0.001200 YES
Predicted change in Energy=-1.724417D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -52.1723 -0.0939 -0.0119 -0.0026 5.3720 5.9734
Low frequencies --- 6.1299 152.5614 381.0175
</pre>

Imaginary frequency found.

==Cyclohexa-1,3-diene and maleic anhydride: Diels-Alder Cycloaddition==

===Optimisation of Cyclohexa-1,3-diene using "Semi-Empirical/AM1" method===

The Cyclohexa-1,3-diene molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:CYCLOHEXADIENE_OPT_AM1.LOG]]

[[File:Cyclohexadiene_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || CYCLOHEXADIENE_OPT_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || 0.02795815 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005245 a.u.
|-
|'''Dipole Moment''' || 0.4559 Debye
|-
|'''Point Group''' || C2v
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000031 0.000300 YES
Maximum Displacement 0.001095 0.001800 YES
RMS Displacement 0.000274 0.001200 YES
Predicted change in Energy=-2.131341D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of maleic anhydride using "Semi-Empirical/AM1" method===

The maleic anhydride molecule was built on gaussian and an optimisation calculation was run using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file was linked here: [[Media:MALEIC_ANHYDRIDE_SE_AM1.LOG]]

[[File:Malaec_opt_pic.png|200px|right|thumb|Optimised Cyclohexa-1,3-diene]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || MALEIC_ANHYDRIDE_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FOPT
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.12182305 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00018525 a.u.
|-
|'''Dipole Moment''' || 4.5857 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 7.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000328 0.000450 YES
RMS Force 0.000143 0.000300 YES
Maximum Displacement 0.001747 0.001800 YES
RMS Displacement 0.000769 0.001200 YES
Predicted change in Energy=-9.223066D-07
Optimization completed.
-- Stationary point found.
</pre>

===Optimisation of Exo-Transition state===

[[File:TS_guess_pic.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride Exo transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS2_OPT_BERNEY_SE_AM1.LOG‎]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05041985 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00000400 a.u.
|-
|'''Dipole Moment''' || 5.5642 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000011 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000410 0.001800 YES
RMS Displacement 0.000081 0.001200 YES
Predicted change in Energy=-5.320134D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -812.2483 -1.1462 -1.0021 -0.0047 0.3167 1.3147
Low frequencies --- 2.2276 60.8490 123.8618
</pre>

Therefore an imaginary frequency is present at -812.2483 cm^-1, an animation of said frequency is shown below.

[[File:Exo_TS_imag_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Exo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS2_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09537180 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00005960 a.u.
|-
|'''Dipole Moment''' || 4.0209 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 43.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:Exo_ts_Irc_graph.svg|500px|centre]]

[[File:Exo_movie_ts.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS2_IRC_MINIMISE.LOG]]

[[File:EXO_ts_minimised_pic.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS2_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.15990937 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00001528 a.u.
|-
|'''Dipole Moment''' ||5.2575 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000699 0.001800 YES
RMS Displacement 0.000135 0.001200 YES
Predicted change in Energy=-4.346033D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.9529 -3.6263 -2.6022 -0.0027 0.0805 0.1094
Low frequencies --- 70.6002 148.5920 168.7367
</pre>

Imaginary frequency found.

===Optimisation of Endo-Transition state===
[[File:Input_guess_ts.png|250px|right|thumb|Guess input structure of Cyclohexa-1,3-diene/maleic anhydride transition state]]

A guess structure of the transition state between Cyclohexa-1,3-diene and maleic anhydride was built on gaussian, shown to the right.
This structure was then optimised to a (Berney) transition state using the "opt+freq" job type, the "Semi Empirical/AM1" method and key words "Opt=NoEigen. The calculation was run through gaussian and the output file linked here: [[Media:TS1_OPT_BERNY_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_OPT_BERNEY_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.05150451 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002717 a.u.
|-
|'''Dipole Moment''' || 6.1649 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000058 0.000450 YES
RMS Force 0.000011 0.000300 YES
Maximum Displacement 0.001631 0.001800 YES
RMS Displacement 0.000394 0.001200 YES
Predicted change in Energy=-9.173070D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -806.7387 -1.5281 -0.3702 -0.0104 0.3966 2.1554
Low frequencies --- 3.1366 62.4555 111.7326
</pre>

Therefore an imaginary frequency is present at -806.7387 cm^-1, an animation of said frequency is shown below.

[[File:Endo_ts_imaginary_vib.gif|250px|centre]]

===Intrinsic Reaction Coordinate of Endo-Transition state===

The IRC method was used to find the product structure by following the minimum energy pathway down to the minimum on the Potential energy surface. The job type used was "IRC", parameters were set to compute the reaction both ways, to calculated the force constant "always" at each point along the IRC and to compute 100 points along the IRC. The calculation was run through gaussian and the output was linked here: [[Media:TS1_IRC_SE_AM1.LOG]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_SE_AM1
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || IRC
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' Total Energy''' || -0.09427768 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00006661 a.u.
|-
|'''Dipole Moment''' || 4.8193 Debye
|-
|'''Point Group''' || C1
|-
|'''Calculation Time''' || 3 minutes 56.0 seconds
|}

Below are the graphs presenting the IRC calculation path:

[[File:IRC_graph_endo_ts.svg|500px|centre]]

[[File:Endo_ts_movie.gif]]

However the true minimum has yet to be reached, therefore an optimisation was conducted on the lowest energy structure of the IRC calculation using the "Semi-Empirical/AM1" method. The calculation was run through gaussian and the output file linked here: [[Media: TS1_IRC_MINIMISE.LOG]]

[[File:Minimised_endo_ts.png|250px|right|thumb|Minismised product molecule]]

A summary of the calculation is tabulated below.

{| class="wikitable" border="1"
|+
|-
| '''File Name''' || TS1_IRC_MINIMISE
|-
| '''File Type''' || .log
|-
| '''Calculation Type''' || FREQ
|-
| '''Calculation Method''' || RAM1
|-
| '''Basis Set''' || ZDO
|-
| '''Charge''' || 0
|-
| ''' Spin''' || Singlet
|-
| ''' E(RAM1)''' || -0.16017077 a.u.
|-
| ''' RMS Gradient Norm''' || 0.00002206 a.u.
|-
|'''Dipole Moment''' || 5.5836 Debye
|-
|'''Point Group''' || Cs
|-
|'''Calculation Time''' || 3.0 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000075 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.000940 0.001800 YES
RMS Displacement 0.000183 0.001200 YES
Predicted change in Energy=-7.998715D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.9303 -4.0490 -3.3054 -0.0034 0.0475 0.1101
Low frequencies --- 72.1115 148.1370 167.3502
</pre>

Imaginary frequency found.

<references>

</references>