ChemWiki - User contributions [en]

Rep:Mod:js1007physical

2010-02-22T16:51:29Z

Js1007: /* Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b. The HOMO is anti-symmetric and the LUMO is symmetric.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}

===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclohexa-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt freq am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of each molecule were visualised. The HOMO and LUMO are shown below in figures. 1f to 1i.
{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}
Figures. 1j and 1l show the endo and exo transition structure for the reaction of Maleic anhydride with Cyclohexa-1,3-diene and the table shows the through space distance between the -(C=O)-O-(C=O)- fragment of the anhydride and the carbon atoms on the opposite -CH2-CH2-/ -CH=CH- fragment of the diene.
{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
Figures. 1k and 1m are animations of the one imaginary frequency of each transition state. For the endo transition state this was
at -806cm-1 and for the exo transition state this was at -812cm-1.
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}
The table below gives the relative energy of the exo and endo transition state calculated using three different semi empirical approximations. Regardless of which approximation was used the energy of the endo transition state was higher than that of the exo transition state. This was quite unexpected since the reaction is kinectically controlled. To help understand why the energy of the endo transition state is higher than the energy of the exo transition state the molecular orbitals of each transition state were analysed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
The table below shows the HOMO and LUMO of the endo and exo transition states generated using three different semi empirical approximations.

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T16:51:05Z

Js1007: /* Part a: Drawing and optimising Cis butadiene */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b. The HOMO is anti-symmetric and the LUMO is symmetric.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclohexa-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt freq am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of each molecule were visualised. The HOMO and LUMO are shown below in figures. 1f to 1i.
{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}
Figures. 1j and 1l show the endo and exo transition structure for the reaction of Maleic anhydride with Cyclohexa-1,3-diene and the table shows the through space distance between the -(C=O)-O-(C=O)- fragment of the anhydride and the carbon atoms on the opposite -CH2-CH2-/ -CH=CH- fragment of the diene.
{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
Figures. 1k and 1m are animations of the one imaginary frequency of each transition state. For the endo transition state this was
at -806cm-1 and for the exo transition state this was at -812cm-1.
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}
The table below gives the relative energy of the exo and endo transition state calculated using three different semi empirical approximations. Regardless of which approximation was used the energy of the endo transition state was higher than that of the exo transition state. This was quite unexpected since the reaction is kinectically controlled. To help understand why the energy of the endo transition state is higher than the energy of the exo transition state the molecular orbitals of each transition state were analysed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
The table below shows the HOMO and LUMO of the endo and exo transition states generated using three different semi empirical approximations.

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T16:48:32Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclohexa-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt freq am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of each molecule were visualised. The HOMO and LUMO are shown below in figures. 1f to 1i.
{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}
Figures. 1j and 1l show the endo and exo transition structure for the reaction of Maleic anhydride with Cyclohexa-1,3-diene and the table shows the through space distance between the -(C=O)-O-(C=O)- fragment of the anhydride and the carbon atoms on the opposite -CH2-CH2-/ -CH=CH- fragment of the diene.
{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
Figures. 1k and 1m are animations of the one imaginary frequency of each transition state. For the endo transition state this was
at -806cm-1 and for the exo transition state this was at -812cm-1.
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}
The table below gives the relative energy of the exo and endo transition state calculated using three different semi empirical approximations. Regardless of which approximation was used the energy of the endo transition state was higher than that of the exo transition state. This was quite unexpected since the reaction is kinectically controlled. To help understand why the energy of the endo transition state is higher than the energy of the exo transition state the molecular orbitals of each transition state were analysed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
The table below shows the HOMO and LUMO of the endo and exo transition states generated using three different semi empirical approximations.

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T16:46:36Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclohexa-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt freq am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of each molecule were visualised. The HOMO and LUMO are shown below in figures. 1f to 1i.
{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}
Figures. 1j and 1l show the endo and exo transition structure for the reaction of Maleic anhydride with Cyclohexa-1,3-diene and the table shows the through space distance between the -(C=O)-O-(C=O)- fragment of the anhydride and the carbon atoms on the opposite -CH2-CH2-/ -CH=CH- fragment of the diene.
{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
Figures. 1k and 1m are animations of the one imaginary frequency of each transition state. For the endo transition state this was
at -806cm-1 and for the exo transition state this was at -812cm-1.
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}
The table below gives the relative energy of the exo and endo transition state calculated using three different semi empirical approximations. Regardless of which approximation was used the energy of the endo transition state was higher than that of the exo transition state. This was quite unexpected since the reaction is kinectically controlled. To help understand why the energy of the endo transition state is higher than the energy of the exo transition state the molecular orbitals of each transition state were analysed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
The table below shows the HOMO and LUMO of the endo and exo transition states generated using three different semi empirical approximations.

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}
The table below gives the relative energy of the exo and endo transition state calculated using three different semi empirical approximations. Regardless of which approximation was used the energy of the endo transition state was higher than that of the exo transition state.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T16:41:28Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclohexa-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt freq am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of each molecule were visualised. The HOMO and LUMO are shown below in figures. 1f to 1i.
{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}
Figures. 1j and 1l show the endo and exo transition structure for the reaction of Maleic anhydride with Cyclohexa-1,3-diene and the table shows the through space distance between the -(C=O)-O-(C=O)- fragment of the anhydride and the carbon atoms on the opposite -CH2-CH2-/ -CH=CH- fragment of the diene.
{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
Figures. 1k and 1m are animations of the one imaginary frequency of each transition state. For the endo transition state this was
at -806cm-1 and for the exo transition state this was at -812cm-1.
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}
The table below gives the relative energy of the exo and endo transition state calculated using three different semi empirical approximations. Regardless of which approximation was used the energy of the endo transition state was higher than that of the exo transition state. This was quite unexpected since the reaction is kinectically controlled. To help understand why the energy of the endo transition state is higher than the energy of the exo transition state the molecular orbitals of each transition state were analysed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
The table below shows the HOMO and LUMO generated

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}
The table below gives the relative energy of the exo and endo transition state calculated using three different semi empirical approximations. Regardless of which approximation was used the energy of the endo transition state was higher than that of the exo transition state.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T16:34:40Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclohexa-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt freq am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of each molecule were visualised. The HOMO and LUMO are shown below in figures. 1f to 1i.
{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}
Figures. 1j and 1l show the endo and exo transition structure for the reaction of Maleic anhydride with Cyclohexa-1,3-diene and the table shows the through space distance between the -(C=O)-O-(C=O)- fragment of the anhydride and the carbon atoms on the opposite -CH2-CH2-/ -CH=CH- fragment of the diene.
{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
Figures. 1k and 1m are animations of the one imaginary frequency of each transition state. For the endo transition state this was
at -806cm-1 and for the exo transition state this was at -812cm-1.
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}
The table below gives the relative energy of the exo and endo transition state calculated using three different semi empirical approximations. Regardless of which approximation was used the energy of the endo transition state was higher than that of the exo transition state.
{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T16:25:54Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclohexa-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt freq am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of each molecule were visualised. The HOMO and LUMO are shown below in figures. 1f to 1i.
{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}
Figures. 1j and 1l show the endo and exo transition structure for the reaction of Maleic anhydride with Cyclohexa-1,3-diene and the table shows the through space distance between the -(C=O)-O-(C=O)- fragment of the anhydride and the carbon atoms on the opposite -CH2-CH2-/ -CH=CH- fragment of the diene.
{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
Figures. 1k and 1m are animations of the one imaginary frequency of each transition state. For the endo transition state this was

{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T16:01:31Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclohexa-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt freq am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of each molecule were visualised. The HOMO and LUMO are shown below in figures. 1f to 1i.
{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}
Figures. 1j and 1l show the endo and exo transition structure for the reaction of Maleic anhydride with Cyclohexa-1,3-diene and the table shows the through space distance between the -(C=O)-O-(C=O)- fragment of the anhydride and the carbon atoms on the opposite -CH2-CH2-/ -CH=CH- fragment of the diene.
{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
Figures. 1k and 1m are animations of the one imaginary frequency of each transition state.

{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T15:52:29Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclohexa-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt freq am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of each molecule were visualised. The HOMO and LUMO are shown below in figures. 1f to 1i.
{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}
Figures. 1j and 1l show the endo and exo transition structure for the reaction of Maleic anhydride with Cyclohexa-1,3-diene and the table shows the through space distance between the -(C=O)-O-(C=O)- fragment of the anhydride and the carbon atoms on the opposite -CH2-CH2-/ -CH=CH- fragment of the diene.
{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
Figures. 1k and 1m are animations of the

{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T15:51:04Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclohexa-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt freq am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of each molecule were visualised. The HOMO and LUMO are shown below in figures. 1f to 1i.
{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}
Figures. 1j and 1l show the endo and exo transition structure for the reaction of Maleic anhydride with Cyclohexa-1,3-diene and the table shows the through space distance between the -(C=O)-O-(C=O)- fragment of the anhydride and the carbon atoms on the opposite -CH2-CH2-/ -CH=CH- fragment of the diene.
{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T15:48:15Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclo-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt freq am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of each molecule were visualised. The HOMO and LUMO are shown below in figures. 1f to 1i.
{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}
Figures. 1j and 1l show the endo and exo transition structure for the reaction of Maleic anhydride and Cyclo-1,3-diene and the table shows the through space distance between the -(C=O)-O-(C=O)- fragment of the anhydride and the carbon atoms of the opposite -CH2-CH2-/ -CH=CH- fragment of the diene.
{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T15:38:29Z

Js1007: /* The Diels Alder Cycloaddition */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclo-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt freq am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of each molecule were visualised. The HOMO and LUMO are shown below in figures. 1f to 1i.

{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T15:36:17Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene undergo a Diels Alder reaction to form either the endo or exo product. Maleic anhydride and Cyclo-1,3-diene were drawn in GaussView 5 and optimised using the AM1 semi-empirical molecular orbital method. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt freq am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals

{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T15:18:57Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
Maleic anhydride and Cyclohexa-1,3-diene

{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T15:16:58Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
{|
|[[Image:Js1007cyclohomo.JPG|thumb|180px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T15:15:42Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
{|
|[[Image:Js1007cyclohomo.JPG|thumb|200px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|200px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T15:07:49Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|335px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|210px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T15:06:55Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|430px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|315px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|210px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T15:06:08Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|420px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irctotalenergy.jpg|thumb|310px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|}
{|
|[[Image:Js1007ircii.JPG|thumb|420px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irciii.JPG|thumb|420px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|310px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|300px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|210px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T15:03:30Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|370px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|370px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|370px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px|Graph showing how the total energy changes IRC N=50 ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px|Graph showing how the gradient of the PES changes IRC N=50 ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px|Graph showing how the total energy changes IRC Calculating force constants at every step ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px|Graph showing how the gradient of the PES changes IRC Calculating force constants at every step]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|210px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T14:55:18Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|370px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|370px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|370px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|210px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T14:53:59Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|210px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|left|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007exobondangles.jpg|thumb|right|250px|Fig. 1l Exo transition state: Distances between atoms ]]
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}
|}
{|
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T14:51:49Z

Js1007: /* Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===
{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|210px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|200px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|200px|Fig. 1i Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|270px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Fig. 1l Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|270px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|200px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|200px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|200px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|200px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|200px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|200px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|200px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|200px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|200px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|200px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|200px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|200px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T14:49:57Z

Js1007: /* Part a: Drawing and optimising Cis butadiene */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b: Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction pathway===
{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Fig. 1c Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Fig. 1d Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Fig. 1e Transition state: Imaginary vibration ]]
|}
===Part c: Studying the regioselectivity of the Diels Alder Reaction- Endo and Exo===

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Fig. 1f Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Fig. 1g Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Fig. 1h Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Fig. 1i Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Fig. 1j Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Fig. 1k Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Fig. 1l Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Fig. 1m Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T14:42:10Z

Js1007: /* Part a: Drawing and optimising Cis butadiene */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

===Part b:

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T14:40:04Z

Js1007: /* The Diels Alder Cycloaddition */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==
===Part a: Drawing and optimising Cis butadiene===
A molecule of Cis butadiene was drawn in GaussView 5 and then optimised using the AM1 semi empirical molecular orbital method.
The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt am1 geom=connectivity</pre>
|}
Once this calculation had finished running, the molecular orbitals of the molecule were visualised. The HOMO and LUMO are shown below in figures. 1a and 1b.
{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Fig. 1a Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Fig. 1b Cis butadiene LUMO ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}

==References==
<references />

Rep:Mod:js1007physical

2010-02-22T14:32:28Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

===Part g: Calculating activation energies===

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-22T14:28:57Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below. I saw no point in running the IRC again but with a larger number of points as this would have just found the same minimum geometry as the inital calculation.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-22T14:26:15Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below.
{|
|<pre># opt rhf/3-21g geom=connectivity</pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-22T14:25:56Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below.
{|
|<pre># opt rhf/3-21g geom=connectivity<pre>
|}
{|
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-22T14:25:33Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step. The top line of the .gjf input files for these calculations are given below.
{|
|<pre># opt rhf/3-21g geom=connectivity<pre>
|<pre># irc=(forward,maxpoints=50,calcall) rhf/3-21g geom=connectivity</pre>
|}

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-22T14:20:15Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.
The following IRC calculation was then run. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># irc=(forward,maxpoints=50,calcfc) rhf/3-21g scrf=check guess=tcheck</pre>
|}
This calculation found a minimum geometry after 25 steps. The calculation was run again, once taking the last point on the IRC and running a normal minimization and once redoing the IRC only this time calculating force constants at every step.

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T21:01:08Z

Js1007: /* Optimizing the "Chair" and "Boat" Transition Structures */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the starting structure was opened in GaussView 5.

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:58:47Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier for the TS(Berny) optimisation of the chair transition state was opened in GaussView 5.

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:34:35Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file obtained earlier

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:33:11Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file for the optimised chair

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:32:07Z

Js1007: /* Part f: Intrinsic Reaction Coordinate calculation */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===
The .chk output file for the optimised

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:26:26Z

Js1007: /* Part e: Optimising the boat transition structure */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
===Part f: Intrinsic Reaction Coordinate calculation===

{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:24:52Z

Js1007: /* Part e: Optimising the boat transition structure */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|330px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|380px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:24:19Z

Js1007: /* Part e: Optimising the boat transition structure */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|300px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|360px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:23:52Z

Js1007: /* Part e: Optimising the boat transition structure */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|250px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|330px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:23:21Z

Js1007: /* Part e: Optimising the boat transition structure */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometry of both structures was not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of its one imaginary frequency at -839cm-1.
{|
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|300px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|300px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:21:22Z

Js1007: /* Part b: Optimising the starting structure to a TS(Berny) */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -818cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometries were not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of the one imaginary frequency at -839cm-1
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|250px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|250px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:21:07Z

Js1007: /* Part e: Optimising the boat transition structure */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -817.84cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometries were not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of the one imaginary frequency at -839cm-1
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|250px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|250px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:19:31Z

Js1007: /* Optimizing the "Chair" and "Boat" Transition Structures */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -817.84cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometries were not close enough to the boat transition structure for the QST2 method to locate it. The starting structures were modified so that the calculation could be run again without failing. Figure. 1h shows how the modified structures looked.
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|300px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|300px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|}
This time the calculation did not fail and the boat transition structure was located. This is shown below along with an animation of the one imaginary frequency at
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|250px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|250px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:08:15Z

Js1007: /* Part e: Optimising the boat transition structure */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -817.84cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because the starting geometries were not close enough to the boat transition structure. The calculation was run again but this time starting with structures shown in figure. 1h. This time the calculation did not fail. The optimised structure is shown in figure. 1j.

{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|250px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|250px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|250px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|250px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Fig. 1j Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:00:47Z

Js1007: /* Part e: Optimising the boat transition structure */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -817.84cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183}}). The reason why it failed is because in order for the QST2 method to be able to locate the structure of the boat transition state the starting geometry must be better.

{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|250px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|250px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|250px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|250px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T20:00:16Z

Js1007: /* Part e: Optimising the boat transition structure */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -817.84cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed ({{DOI|10042/to-4183#}}). The reason why it failed is because in order for the QST2 method to be able to locate the structure of the boat transition state the starting geometry must be better.

doi for part e expected to fail /10042/to-4183#
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|250px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|250px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|250px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|250px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T19:58:15Z

Js1007: /* Part e: Optimising the boat transition structure */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -817.84cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5. Add MolGroup from the file tab was selected and the optimised structure was pasted into a new window twice. After labelling the atoms the structures were orientated as shown in figure. 1g and then optimised again, this time using the QST2 method. The top line of the .gjf input file for this optimisation is given below.
{|
<pre># opt=qst2 freq hf/3-21g geom=connectivity</pre>
|}

This calculation failed (. The reason why it failed is because in order for the QST2 method to be able to locate the structure of the boat transition state the starting geometry must be better.

doi for part e expected to fail /10042/to-4183#
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|250px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|250px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|250px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|250px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />

Rep:Mod:js1007physical

2010-02-21T19:42:41Z

Js1007: /* Part e: Optimising the boat transition structure */

=Module 3=
==The Cope Rearrangement Tutorial==
==Optimizing the Reactants and Products==

===Part a: Drawing and optimising 1,5-hexadiene with an "anti" linkage===

A molecule of 1,5-hexadiene with the central four carbon atoms in an anti-periplanar conformation (dihedral angle of 1800) was drawn using GaussView 5. This molecule was then cleaned using the clean tab in the edit menu before being optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened and information about the energy and symmetry of the optimised structure was noted. The total energy of the optimised structure was -231.69260235a.u. and the point group was C2. From looking at the energy of this structure and its point group and comparing these values with that in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the anti (1). Figure. 1a and b below show the optimised anti structure and the summary table for this optimisation respectively.
{|
|[[Image:Js1007anti(parta).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007anti(parta).mol</uploadedFileContents>
<text> Fig. 1a Anti (1) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007anti(parta)summarytable.JPG|thumb|200px|Fig. 1b Anti (1) 1,5-hexadiene Summary Table ]]
|}

===Part b and c: Drawing and optimising a molecule of 1,5-hexadiene with a "gauche" linkage and predicting the lowest energy conformation of 1,5-hexadiene===
Another molecule of 1,5-hexadiene was drawn but this time with the central four carbon atoms in a gauche conformation (dihedral angle this time of 600). Just like for the anti structure, the gauche structure was cleaned using the clean tab in the edit menu and then optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The total energy of this optimised structure was -231.69266121a.u. and the point group was C1. By comparing these values with those in appendix 1<ref>http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3</ref> it is clear that the structure obtained from this optimisation is the gauche (3).
{|
|[[Image:Js1007gauche(partb).JPG|thumb|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007gauche(partb).mol</uploadedFileContents>
<text>Fig. 1c Gauche (3) 1,5-hexadiene</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007gauche(partb)summarytable.JPG|thumb|200px|Fig. 1d Gauche (3) 1,5-hexadiene Summary Table ]]
|}
Quite unexpectedly the gauche (3) structure is lower in energy than the anti (1) structure by 0.15kJ/mol. It is not initially clear why this is the case as you would expect the greater steric clash between the two alkene groups in the gauche structure to make its energy much higher than that of the anti structure (see figure. 1e). It was thought that by analysing the molecular orbitals in both structures the reason why the gauche structure does have a lower energy would become much clearer. Figures. 1f to 1i show these orbitals. From looking at figures. 1g and 1i it is clear that the reason why the gauche structure has a lower energy is due to a stabilising π-π interaction between the two alkene groups which is not present in the anti structure. This interaction is present in only the gauche structure as this is the only structure in which the alkene groups are close enough to interact and are correctly orientated for this interaction. There is also a stabilising interaction (hyperconjugation) between the σ C-C and the π* of the alkene in the gauche structure which is another reason for its lower energy.
{|
|[[Image:Js1007gaucheandantisawhorse.JPG|thumb|250px|Fig. 1e Steric clash between alkene groups ]]
|[[Image:Js1007antilumo.JPG|thumb|200px|Fig. 1f Anti (1) LUMO ]]
|[[Image:Js1007antihomo.JPG|thumb|200px|Fig. 1g Anti (1) HOMO ]]
|[[Image:Js1007gauchelumo.JPG|thumb|200px|Fig. 1h Gauche (3) LUMO ]]
|[[Image:Js1007gauchehomoannotated.JPG|thumb|200px|Fig. 1i Gauche (3) HOMO ]]
|}

===Part e and f: Drawing and optimising the "anti (2)" structure of 1,5-hexadiene using different approximations===
The anti (2) structure of 1,5-hexadiene was drawn and optimised using the hartree fock approximation, HF and the split valence basis set, 3-21G. The top line of the .gjf input file for this optimisation is shown below along with the optimised structure.
{|
|<pre>%mem=10500MB
# opt hf/3-21g geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(part_e)output.jpg|thumb|400px|Fig. 1j Anti (2) 1,5-hexadiene HF/3-21G ]]
|[[Image:Js1007antiecorrect.jpg|thumb|400px|Fig. 1k Bond lengths HF/3-21G ]]
|[[Image:Js1007anti2etable.JPG|thumb|250px|Fig. 1l Summary table HF/3-21G ]]
|}
Once this calculation had finished running the structure was reoptimised using a different basis set, one now based on the Born-Oppenheimer approximation and a polarised basis set that now allowed the shape of the orbitals to change. The approximation and basis set used were DFT B3LYP and 6-31G* respectively. The top line of the .gjf input file for this reoptimisation is shown below along with the reoptimised structure.
{|
|<pre>%mem=10500MB
# opt b3lyp/6-31g(d) geom=connectivity</pre>
|}
{|
|[[Image:Js1007anti2(partf)output.jpg|thumb|400px|Fig. 1m Anti (2) 1,5-hexadiene B3LYP/6-31G* ]]
|[[Image:Js1007antif.jpg|thumb|400px|Fig. 1n Bond lengths B3LYP/6-31G* ]]
|[[Image:Js1007anti2ftable.JPG|thumb|250px|Fig. 1o Summary table B3LYP/6-31G* ]]
|}
The total energy of the anti (2) HF/3-21G structre was -231.69253528a.u. and the total energy of the anti (2) B3LYP/6-31G* structure was -234.61170276a.u. Since these values were obtained by using a different type of approximation and basis set they cannot be compared.

Table below shows how bond lengths changed when the type of approximation and basis set used were changed.
{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) HF/3-21G'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Anti (2) B3LYP/6-31G*'''
|-
| C14-C7||1.3161||C14-C7||1.3335
|-
| C4-C7||1.5089||C7-C4||1.5042
|-
| C4-C1||1.5528||C4-C1||1.5481
|-
| C1-C9||1.5089||C1-C9||1.5042
|-
| C9-C11||1.3161||C9-C11||1.3335
|-
|
|}

===Part g: Running a frequency calculation on the optimised B3LYP/6-31G* anti (2) structure of 1,5-hexadiene===
A frequency calculation on the B3LYP/6-31G* optimised anti (2) structure of 1,5-hexadiene was set up using GaussView 5. The top line of the .gjf input file for this calculation is shown below.
{|
|<pre># freq b3lyp/6-31g(d) geom=connectivity</pre>
|}
Once this calculation had finished running the .log output file was opened and information about the vibrations of anti (2) 1,5-hexadiene was obtained. A table listing these vibrations is given below along with the infra red spectrum. The fact that there are no negative (imaginary) frequencies listed indicates that the structure was successfully optimised earlier.
{|
|[[Image:Js1007anti2frequencyvibtable.JPG|thumb|250px|Fig. 1p Anti (2) 1,5-hexadiene: Table of vibrations ]]
|[[Image:Js1007anti2irspectrum.jpg|thumb|500px|Fig. 1q Anti (2) 1,5-hexadiene: IR spectrum ]]
|}
The table below shows the values of different energy terms that were found in the thermochemistry section of the .log output file. These quanties were re-calculated at 0K and are also shown in the table. To re-calculate these terms at 0K the frequency calculation was run again but this time with Freq=ReadIsotopes added to the additional keyword section and information about the temperature, atmospheric pressure and mass of the atoms present manually added to the bottom of the input file.

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Energy term'''
| align="center" style="background:#f0f0f0;"|'''Energy @298.15K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Energy @ 0K / (a.u.)'''
| align="center" style="background:#f0f0f0;"|'''Difference'''
|-
| The sum of the electronic and zero-point energies||-234.469212||-234.468775||0.000437
|-
| The sum of electronic and thermal energies||-234.461856||-234.461429||0.000427
|-
| The sum of electronic and thermal enthalpies||-234.460912||-234.460485||0.000427
|-
| The sum of electronic and thermal free energies||-234.500821||-234.500372||0.000449
|-
|
|}

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

===Part a: Drawing an allyl fragment (CH2CHCH2), optimising it and using it to then form a reasonably good starting structure for finding transition states===

The allyl fragment (CH2CHCH2) was drawn in GaussView 5 and then optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Figure. 1a shows this optimised fragment. By copying and pasting this fragment a couple of times and carefully orientating each one so that they were approximately 2.2A apart a reasonably good starting structure for finding the chair transition structure was formed. This structure is shown is figure. 1b.
{|
|[[Image:Js1007opt(a)allylfragment.JPG|thumb|250px|Fig. 1a Optimised allyl fragment HF/3-21G ]]
|[[Image:Js1007opt(a)twoallylfragments.jpg|thumb|230px|Fig. 1b Two allyl fragments: Chair transition state (guess) ]]
|}

===Part b: Optimising the starting structure to a TS(Berny)===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Optimisation to a minimum was changed to optimisation to a TS(Berny), force constants were set so that they would be calculated once and Opt=NoEigen was added to the additional keywords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=(calcfc,ts,noeigen) freq hf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below along with a table of the vibrations of the molecule and an animation of the one imaginary frequency at -817.84cm-1. As can been seen by looking at this animation the imaginary frequency corresponds to the Cope rearrangement.
{|
|[[Image:Js1007opt(b)anglesandlengths.jpg|thumb|230px|Fig. 1c Chair transition state HF/3-21G TS Berny: Bond angles and lengths ]]
|[[Image:Js1007opt(partb)outputshowingvib.JPG|thumb|250px|Fig. 1d Chair transition state HF/3-21G: Imaginary vibration ]]
|[[Image:Js1007opt(partb)vibtable.JPG|thumb|250px|Fig. 1e Chair transition state: Table of vibrations ]]
|}

===Part c and d: Optimising the starting structure using the frozen coordinate method===
The structure in figure. 1b was optimised using the hartree fock approximation, HF and split valence basis set, 3-21G. Using the Redundant Coordinator Editor option in the edit tab, the distance between the terminal carbon atoms was frozen to 2.2A. Optimisation to a minimum was selected and Opt=ModRedundant was added to the additional kewords section. The top line of the .gjf input file for this optimisation is given below.
{|
|<pre># opt=modredundant hf/3-21g geom=connectivity</pre>
|}
Once this calculation had finished running the .chk output file was opened. From this file the optimisation was carried out again. This time certain settings in the Redundant Coordinator Editor were changed, optimisation to a minimum was changed to optimisation to a TS(Berny) and calculate force constants was set to never. The top line of the .gjf input file for this calculation is given below.
{|
|<pre># opt=(ts,modredundant) rhf/3-21g geom=connectivity</pre>
|}
The optimised structure is shown below.
{|
|[[Image:Js1007opt(d)anglesandlengths.jpg|thumb|250px|Fig. 1f Chair transition state HF/3-21G Redundant coordinator: Bond angles and lengths ]]
|}
===Part e: Optimising the boat transition structure===
The .chk output file for the optimised anti (2) structure of 1,5-hexadiene obtained earlier was opened in GaussView 5 and then copied and pasted into a new window. By selecting Add to MolGroup from the file tab this molecule was then copied and pasted again into the same window in such a way that meant the two structures could be viewed simultaneously or individually depending on what was desired. Labels were then added to both of the structures, numbering the atoms, before they were orientated as shown in figure. 1g.

doi for part e expected to fail /10042/to-4183#
{|
|[[Image:Js1007opt(e)expectedtofailinput.JPG|thumb|250px|Fig. 1g Boat transition state before optimised using TS(QST2): Expected to fail ]]
|[[Image:Js1007opt(e)expectedtoworkinput.JPG|thumb|250px|Fig. 1h Boat transition state before optimised using TS(QST2): Expected to work ]]
|[[Image:Js1007opt(e)expectedtoworkoutputshowingvib.JPG|thumb|250px|Fig. 1i Boat transition state TS(QST2): Imaginary vibration ]]
|[[Image:Js1007parteoutputworked.JPG|thumb|250px|250px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007parteoutputworked.mol</uploadedFileContents>
<text>Boat transition state after optimisation using TS(QST2)</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irc.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irc.mol</uploadedFileContents>
<text>Chair transition structure IRC where number of points along the IRC = 50</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007irciii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007irciii.mol</uploadedFileContents>
<text>Chair transition structure IRC calculating force constants at every step</text>
</jmolAppletButton>
</jmol> ]]
|[[Image:Js1007ircii.JPG|thumb|350px|<jmol>
<jmolAppletButton>
<uploadedFileContents>Js1007ircii.mol</uploadedFileContents>
<text>Chair transition structure IRC running normal minimisation</text>
</jmolAppletButton>
</jmol> ]]
|}
{|
|[[Image:Js1007irctotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007ircgradient.jpg|thumb|250px| ]]
|[[Image:Js1007irciiitotalenergy.jpg|thumb|250px| ]]
|[[Image:Js1007irciiigradient.jpg|thumb|250px| ]]
|}

==The Diels Alder Cycloaddition==

{| {{table}}
| align="center" style="background:#f0f0f0;"|'''Distance between carbon atoms'''
| align="center" style="background:#f0f0f0;"|'''Endo Transition State'''
| align="center" style="background:#f0f0f0;"|'''Distance between carbons atoms'''
| align="center" style="background:#f0f0f0;"|'''Exo Transition State'''
|-
| C17-C4||2.89194||C17-C12||2.94501
|-
| C15-C1||2.89287||C15-C9||2.94498
|-
| C20-C3||2.16193||C20-C2||2.1703
|-
| C22-C2||2.1628||C22-C3||2.17035
|-
|
|}

{|
|[[Image:Js1007cisbutadienehomo.JPG|thumb|250px|Cis butadiene HOMO ]]
|[[Image:Js1007cisbutadienelumo.JPG|thumb|250px|Cis butadiene LUMO ]]
|}

{|
|[[Image:Js1007transitionstatehomo.JPG|thumb|250px|Transition state HOMO ]]
|[[Image:Js1007transitionstatelumo.JPG|thumb|250px|Transition state LUMO ]]
|[[Image:Js1007transitionstateshowingvib(partii).JPG|thumb|250px|Transition state: Imaginary vibration ]]
|}

{|
|[[Image:Js1007cyclohomo.JPG|thumb|250px|Cyclohexa-1,3-diene HOMO ]]
|[[Image:Js1007cyclolumo.JPG|thumb|250px|Cyclohexa-1,3-diene LUMO ]]
|[[Image:Js1007maleichomo.JPG|thumb|250px|Maleic Anhydride HOMO ]]
|[[Image:Js1007maleiclumo.JPG|thumb|250px|Maleic anhydride LUMO ]]
|}

{|
|[[Image:Js1007endobondangles.jpg|thumb|250px|Endo transition state: Distances between atoms ]]
|[[Image:Js1007endoshowingvib.JPG|thumb|250px|Endo transition state: Imaginary vibration ]]
|[[Image:Js1007exobondangles.jpg|thumb|250px|Exo transition state: Distances between atoms ]]
|[[Image:Js1007exoshowingvib.JPG|thumb|250px|Exo transition state: Imaginary vibration ]]
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''ENDO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''EXO TRANSITION STATE'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| '''AM1'''||[[Image:Js1007endohomo.JPG|thumb|250px|Endo transition state HOMO AM1 ]]||[[Image:Js1007endolumo.JPG|thumb|250px|Endo transition state LUMO AM1 ]]||[[Image:Js1007exohomo.JPG|thumb|250px|Exo transition state HOMO AM1 ]]||[[Image:Js1007exolumo.JPG|thumb|250px|Exo transition state LUMO AM1 ]]
|-
| '''DFT'''||[[Image:Js1007endodfthomo.JPG|thumb|250px|Endo transition state HOMO DFT ]]||[[Image:Js1007endodftlumo.JPG|thumb|250px|Endo transition state LUMO DFT ]]||[[Image:Js1007exodfthomo.JPG|thumb|250px|Exo transition state HOMO DFT ]]||[[Image:Js1007exodftlumo.JPG|thumb|250px|Exo transition state LUMO DFT ]]
|-
| '''MP2'''||[[Image:Js1007endomp2homo.JPG|thumb|250px|Endo transition state HOMO MP2 ]]||[[Image:Js1007endomp2lumo.JPG|thumb|250px|Endo transition state LUMO MP2 ]]||[[Image:Js1007exomp2homo.JPG|thumb|250px|Exo transition state HOMO MP2 ]]||[[Image:Js1007exomp2lumo.JPG|thumb|250px|Exo transition state LUMO MP2 ]]
|-
|
|}

{| {{table}}
| align="center" style="background:#f0f0f0;"|''''''
| align="center" style="background:#f0f0f0;"|'''Endo transition state'''
| align="center" style="background:#f0f0f0;"|'''Exo transition state'''
|-
| '''AMI'''||-0.05150453||-0.05041982
|-
| '''DFT'''||-612.4954778||-612.4909815
|-
| '''MP2'''||-610.8362244||-610.8308724
|-
|
|}
==References==
<references />