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Rep:Module3:AYKLeung

2010-12-17T16:50:39Z

Ayl08: /* Cycloaddition between Maleic Anhydride with Cyclohexadiene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above.
The new bonds formed in the transition state is found to be 2.12Å, which is longer than any C-C bond or the Van der Waals radius (1.70Å). The original sigma bonds are shortened from a typical 1.54Å (Csp3-Csp3) to 1.40Å, and the double bond of ethylene about 1.38Å, which is about 0.04Å longer than a typical C=C (Csp2-Csp2) bond, which is 1.34Å

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

{| class="wikitable" border="1"
|+ ''Table 9: HOMO & LUMO Cyclohexene and its energies ''
!HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cyclohexene ||[[image:AYK_CyclohexeneHOMO.png|200px]]||-0.34380||Symmetric||[[image:AYK_CyclohexeneLUMO.png|200px]] ||0.01707||Asymmetric
|-
|}
Uploaded on D-Space:{{DOI|10042/to-6330}}

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====
[[image:AYK_Reaction_MechEndoExo.png]]

The exo product should be thermodynamically the major product due lower energy, but in real life it is the endo product that dominates.<ref>W.C. Herndon, C.R. Grayson, J.M. Manion, ''J. Am. Chem. Soc..'', 2002, '''124''', 1130 {{DOI|10.1021/jo01278a003}} </ref>
This could be explained by the [http://users.ox.ac.uk/~mwalter/web_06/year3/peri_I/endo_rule.shtml Endo Addition Rule],image below shows the secondary orbital interactions, where the non-bonding carbons interact with each other, thus lowering the activation energy of the reaction.
[[Image:AYK_molecules2endo.png|center|Secondary orbital interactions]]

{| class="wikitable" border="1"
|+ ''Table 10: HOMO & LUMOs of Maleic Anhydride & hexadiene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry!!LUMO!!LUMO energy (a.u.)!!Symmetry
|-
|Maleic Anhydride||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||Symmetric||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034||Asymmetric
|-
|Hexadiene ||[[image:AYK_CyclohexadieneHOMO.png|200px]]||-0.321||Asymmetric||[[image:AYK_CyclohexadieneLUMO.png|200px]]||0.016||Symmetric
|-
|}

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T16:50:31Z

Ayl08: /* Cycloaddition between Cis-Butadiene and Ethylene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above.
The new bonds formed in the transition state is found to be 2.12Å, which is longer than any C-C bond or the Van der Waals radius (1.70Å). The original sigma bonds are shortened from a typical 1.54Å (Csp3-Csp3) to 1.40Å, and the double bond of ethylene about 1.38Å, which is about 0.04Å longer than a typical C=C (Csp2-Csp2) bond, which is 1.34Å

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

{| class="wikitable" border="1"
|+ ''Table 9: HOMO & LUMO Cyclohexene and its energies ''
!HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cyclohexene ||[[image:AYK_CyclohexeneHOMO.png|200px]]||-0.34380||Symmetric||[[image:AYK_CyclohexeneLUMO.png|200px]] ||0.01707||Asymmetric
|-
|}
Uploaded on D-Space:{{DOI|10042/to-6330}}

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====
[[image:AYK_Reaction_MechEndoExo.png]]

The exo product should be thermodynamically the major product due lower energy, but in real life it is the endo product that dominates.<ref>W.C. Herndon, C.R. Grayson, J.M. Manion, ''J. Am. Chem. Soc..'', 2002, '''124''', 1130 {{DOI|10.1021/jo01278a003}} </ref>
This could be explained by the [http://users.ox.ac.uk/~mwalter/web_06/year3/peri_I/endo_rule.shtml Endo Addition Rule],image below shows the secondary orbital interactions, where the non-bonding carbons interact with each other, thus lowering the activation energy of the reaction.
[[Image:AYK_molecules2endo.png|center|Secondary orbital interactions]]

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of Maleic Anhydride & hexadiene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry!!LUMO!!LUMO energy (a.u.)!!Symmetry
|-
|Maleic Anhydride||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||Symmetric||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034||Asymmetric
|-
|Hexadiene ||[[image:AYK_CyclohexadieneHOMO.png|200px]]||-0.321||Asymmetric||[[image:AYK_CyclohexadieneLUMO.png|200px]]||0.016||Symmetric
|-
|}

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T16:50:11Z

Ayl08: /* Cycloaddition between Maleic Anhydride with Cyclohexadiene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above.
The new bonds formed in the transition state is found to be 2.12Å, which is longer than any C-C bond or the Van der Waals radius (1.70Å). The original sigma bonds are shortened from a typical 1.54Å (Csp3-Csp3) to 1.40Å, and the double bond of ethylene about 1.38Å, which is about 0.04Å longer than a typical C=C (Csp2-Csp2) bond, which is 1.34Å

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMO Cyclohexene and its energies ''
!HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cyclohexene ||[[image:AYK_CyclohexeneHOMO.png|200px]]||-0.34380||Symmetric||[[image:AYK_CyclohexeneLUMO.png|200px]] ||0.01707||Asymmetric
|-
|}
Uploaded on D-Space:{{DOI|10042/to-6330}}

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====
[[image:AYK_Reaction_MechEndoExo.png]]

The exo product should be thermodynamically the major product due lower energy, but in real life it is the endo product that dominates.<ref>W.C. Herndon, C.R. Grayson, J.M. Manion, ''J. Am. Chem. Soc..'', 2002, '''124''', 1130 {{DOI|10.1021/jo01278a003}} </ref>
This could be explained by the [http://users.ox.ac.uk/~mwalter/web_06/year3/peri_I/endo_rule.shtml Endo Addition Rule],image below shows the secondary orbital interactions, where the non-bonding carbons interact with each other, thus lowering the activation energy of the reaction.
[[Image:AYK_molecules2endo.png|center|Secondary orbital interactions]]

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of Maleic Anhydride & hexadiene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry!!LUMO!!LUMO energy (a.u.)!!Symmetry
|-
|Maleic Anhydride||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||Symmetric||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034||Asymmetric
|-
|Hexadiene ||[[image:AYK_CyclohexadieneHOMO.png|200px]]||-0.321||Asymmetric||[[image:AYK_CyclohexadieneLUMO.png|200px]]||0.016||Symmetric
|-
|}

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T16:47:49Z

Ayl08: /* Cycloaddition between Maleic Anhydride with Cyclohexadiene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above.
The new bonds formed in the transition state is found to be 2.12Å, which is longer than any C-C bond or the Van der Waals radius (1.70Å). The original sigma bonds are shortened from a typical 1.54Å (Csp3-Csp3) to 1.40Å, and the double bond of ethylene about 1.38Å, which is about 0.04Å longer than a typical C=C (Csp2-Csp2) bond, which is 1.34Å

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMO Cyclohexene and its energies ''
!HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cyclohexene ||[[image:AYK_CyclohexeneHOMO.png|200px]]||-0.34380||Symmetric||[[image:AYK_CyclohexeneLUMO.png|200px]] ||0.01707||Asymmetric
|-
|}
Uploaded on D-Space:{{DOI|10042/to-6330}}

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====
[[image:AYK_Reaction_MechEndoExo.png]]
The exo product should be the major product due to the lower in energy.

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of Maleic Anhydride & hexadiene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry!!LUMO!!LUMO energy (a.u.)!!Symmetry
|-
|Maleic Anhydride||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||Symmetric||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034||Asymmetric
|-
|Hexadiene ||[[image:AYK_CyclohexadieneHOMO.png|200px]]||-0.321||Asymmetric||[[image:AYK_CyclohexadieneLUMO.png|200px]]||0.016||Symmetric
|-
|}

===References===
<references/>

File:AYK Reaction MechEndoExo.png

2010-12-17T16:47:33Z

Ayl08:

Rep:Module3:AYKLeung

2010-12-17T16:38:38Z

Ayl08: /* Cycloaddition between Maleic Anhydride with Cyclohexadiene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above.
The new bonds formed in the transition state is found to be 2.12Å, which is longer than any C-C bond or the Van der Waals radius (1.70Å). The original sigma bonds are shortened from a typical 1.54Å (Csp3-Csp3) to 1.40Å, and the double bond of ethylene about 1.38Å, which is about 0.04Å longer than a typical C=C (Csp2-Csp2) bond, which is 1.34Å

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMO Cyclohexene and its energies ''
!HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cyclohexene ||[[image:AYK_CyclohexeneHOMO.png|200px]]||-0.34380||Symmetric||[[image:AYK_CyclohexeneLUMO.png|200px]] ||0.01707||Asymmetric
|-
|}
Uploaded on D-Space:{{DOI|10042/to-6330}}

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of Maleic Anhydride & hexadiene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry!!LUMO!!LUMO energy (a.u.)!!Symmetry
|-
|Maleic Anhydride||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||Symmetric||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034||Asymmetric
|-
|Hexadiene ||[[image:AYK_CyclohexadieneHOMO.png|200px]]||-0.321||Asymmetric||[[image:AYK_CyclohexadieneLUMO.png|200px]]||0.016||Symmetric
|-
|}

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T16:37:21Z

Ayl08: /* Cycloaddition between Maleic Anhydride with Cyclohexadiene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above.
The new bonds formed in the transition state is found to be 2.12Å, which is longer than any C-C bond or the Van der Waals radius (1.70Å). The original sigma bonds are shortened from a typical 1.54Å (Csp3-Csp3) to 1.40Å, and the double bond of ethylene about 1.38Å, which is about 0.04Å longer than a typical C=C (Csp2-Csp2) bond, which is 1.34Å

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMO Cyclohexene and its energies ''
!HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cyclohexene ||[[image:AYK_CyclohexeneHOMO.png|200px]]||-0.34380||Symmetric||[[image:AYK_CyclohexeneLUMO.png|200px]] ||0.01707||Asymmetric
|-
|}
Uploaded on D-Space:{{DOI|10042/to-6330}}

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Maleic Anhydride|| ||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034
|-
|Hexadiene|| ||[[image:AYK_CyclohexadieneHOMO.png|200px]]||-0.321||[[image:AYK_CyclohexadieneLUMO.png|200px]]||0.016
|-
|}

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T16:36:32Z

Ayl08: /* Cycloaddition between Cis-Butadiene and Ethylene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above.
The new bonds formed in the transition state is found to be 2.12Å, which is longer than any C-C bond or the Van der Waals radius (1.70Å). The original sigma bonds are shortened from a typical 1.54Å (Csp3-Csp3) to 1.40Å, and the double bond of ethylene about 1.38Å, which is about 0.04Å longer than a typical C=C (Csp2-Csp2) bond, which is 1.34Å

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMO Cyclohexene and its energies ''
!HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cyclohexene ||[[image:AYK_CyclohexeneHOMO.png|200px]]||-0.34380||Symmetric||[[image:AYK_CyclohexeneLUMO.png|200px]] ||0.01707||Asymmetric
|-
|}
Uploaded on D-Space:{{DOI|10042/to-6330}}

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Maleic Anhydride|| ||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034
|-
|Hexadiene|| ||[[image:AYK_HexadieneHOMO.png|200px]]||-0.059||[[image:AYK_HexadieneLUMO.png|200px]]||0.034
|-
|}

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T16:36:09Z

Ayl08: /* Cycloaddition between Cis-Butadiene and Ethylene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above.
The new bonds formed in the transition state is found to be 2.12Å, which is longer than any C-C bond or the Van der Waals radius (1.70Å). The original sigma bonds are shortened from a typical 1.54Å (Csp3-Csp3) to 1.40Å, and the double bond of ethylene about 1.38Å, which is about 0.04Å longer than a typical C=C (Csp2-Csp2) bond, which is 1.34Å

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMO Cyclohexene and its energies ''
!HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cyclohexene ||[[image:AYK_CyclohexeneHOMO.png|200px]]||-0.34380||Symmetric||[[image:AYK_CyclohexeneLUMO.png.png|200px]] ||0.01707||Asymmetric
|-
|}
Uploaded on D-Space:{{DOI|10042/to-6330}}

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Maleic Anhydride|| ||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034
|-
|Hexadiene|| ||[[image:AYK_HexadieneHOMO.png|200px]]||-0.059||[[image:AYK_HexadieneLUMO.png|200px]]||0.034
|-
|}

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T16:35:29Z

Ayl08: /* Cycloaddition between Cis-Butadiene and Ethylene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above.
The new bonds formed in the transition state is found to be 2.12Å, which is longer than any C-C bond or the Van der Waals radius (1.70Å). The original sigma bonds are shortened from a typical 1.54Å (Csp3-Csp3) to 1.40Å, and the double bond of ethylene about 1.38Å, which is about 0.04Å longer than a typical C=C (Csp2-Csp2) bond, which is 1.34Å

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMO Cyclohexene and its energies ''
!HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cyclohexene ||[[image:AYK_CyclohexeneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_CyclohexeneLUMO.png.png|200px]] ||0.01707||Symmetric
|-
|}
Uploaded on D-Space:{{DOI|10042/to-6330}}

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Maleic Anhydride|| ||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034
|-
|Hexadiene|| ||[[image:AYK_HexadieneHOMO.png|200px]]||-0.059||[[image:AYK_HexadieneLUMO.png|200px]]||0.034
|-
|}

===References===
<references/>

File:AYK CyclohexadieneLUMO.png

2010-12-17T16:35:17Z

Ayl08:

File:AYK CyclohexadieneHOMO.png

2010-12-17T16:34:55Z

Ayl08:

Rep:Module3:AYKLeung

2010-12-17T16:31:14Z

Ayl08: /* Cycloaddition between Cis-Butadiene and Ethylene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above.
The new bonds formed in the transition state is found to be 2.12Å, which is longer than any C-C bond or the Van der Waals radius (1.70Å). The original sigma bonds are shortened from a typical 1.54Å (Csp3-Csp3) to 1.40Å, and the double bond of ethylene about 1.38Å, which is about 0.04Å longer than a typical C=C (Csp2-Csp2) bond, which is 1.34Å

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMO Cyclohexene and its energies ''
!HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_CyclohexeneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_CyclohexeneLUMO.png.png|200px]] ||0.01707||Symmetric
|-
|}

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Maleic Anhydride|| ||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034
|-
|Hexadiene|| ||[[image:AYK_HexadieneHOMO.png|200px]]||-0.059||[[image:AYK_HexadieneLUMO.png|200px]]||0.034
|-
|}

===References===
<references/>

File:AYK CyclohexeneHOMO.png

2010-12-17T16:29:45Z

Ayl08:

File:AYK CyclohexeneLUMO.png

2010-12-17T16:20:47Z

Ayl08:

Rep:Module3:AYKLeung

2010-12-17T16:14:21Z

Ayl08: /* Cycloaddition between Cis-Butadiene and Ethylene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above.
The new bonds formed in the transition state is found to be 2.12Å, which is longer than any C-C bond or the Van der Waals radius (1.70Å). The original sigma bonds are shortened from a typical 1.54Å (Csp3-Csp3) to 1.40Å, and the double bond of ethylene about 1.38Å, which is about 0.04Å longer than a typical C=C (Csp2-Csp2) bond, which is 1.34Å

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Maleic Anhydride|| ||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034
|-
|Hexadiene|| ||[[image:AYK_HexadieneHOMO.png|200px]]||-0.059||[[image:AYK_HexadieneLUMO.png|200px]]||0.034
|-
|}

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T16:13:33Z

Ayl08: /* Cycloaddition between Cis-Butadiene and Ethylene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above.
The new bonds formed in the transition state is found to be 2.12Å, which is longer than any C-C bond or the Van der Waals radius (1.70Å). The original sigma bonds are shortened from a typical 1.54Å (C<sp3>-C</sp3> to 1.40Å, and the double bond of ethylene about 1.38Å, which is about 0.04Å longer than a typical C=C (Csp2-Csp2 bond, which is 1.34Å

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Maleic Anhydride|| ||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034
|-
|Hexadiene|| ||[[image:AYK_HexadieneHOMO.png|200px]]||-0.059||[[image:AYK_HexadieneLUMO.png|200px]]||0.034
|-
|}

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T16:11:40Z

Ayl08: /* Cycloaddition between Cis-Butadiene and Ethylene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above.
The bonds formed in the transition state is found to be 2.12Å, which is longer than any C-C bond or the Van der Waals radius. The original sigma bonds are shortened , and the double bond of ethylene about 1.38Å, which is about 0.04Å longer than a typical C=C bond, which is 1.34Å
{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Maleic Anhydride|| ||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034
|-
|Hexadiene|| ||[[image:AYK_HexadieneHOMO.png|200px]]||-0.059||[[image:AYK_HexadieneLUMO.png|200px]]||0.034
|-
|}

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T16:06:43Z

Ayl08: /* Cycloaddition between Cis-Butadiene and Ethylene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetric
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Maleic Anhydride|| ||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034
|-
|Hexadiene|| ||[[image:AYK_HexadieneHOMO.png|200px]]||-0.059||[[image:AYK_HexadieneLUMO.png|200px]]||0.034
|-
|}

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T16:06:25Z

Ayl08: /* Cycloaddition between Cis-Butadiene and Ethylene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Asymmetric||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||Symmetric
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetric||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Asymmetry
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Maleic Anhydride|| ||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034
|-
|Hexadiene|| ||[[image:AYK_HexadieneHOMO.png|200px]]||-0.059||[[image:AYK_HexadieneLUMO.png|200px]]||0.034
|-
|}

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T16:05:48Z

Ayl08: /* Cycloaddition between Cis-Butadiene and Ethylene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! HOMO!! HOMO energy (a.u.)!!Symmetry !!LUMO!!LUMO energy (a.u.) !!Symmetry
|-
|Cis-butadiene ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||Symmetr||[[image:AYK_Cis-butadieneLUMO.png|200px]] ||0.01707||
|-
|Ethylene||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||Symmetry||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284||Symmetry
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Maleic Anhydride|| ||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034
|-
|Hexadiene|| ||[[image:AYK_HexadieneHOMO.png|200px]]||-0.059||[[image:AYK_HexadieneLUMO.png|200px]]||0.034
|-
|}

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T16:04:17Z

Ayl08: /* Cycloaddition between Maleic Anhydride with Cyclohexadiene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||[[image:AYK_Cis-butadieneLUMO.png|200px]]||0.01707
|-
|Ethylene|| ||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Maleic Anhydride|| ||[[image:AYK_Maleic_anhydrideHOMO.png|200px]]||-0.059||[[image:AYK_Maleic_anhydrideLUMO.png|200px]]||0.034
|-
|Hexadiene|| ||[[image:AYK_HexadieneHOMO.png|200px]]||-0.059||[[image:AYK_HexadieneLUMO.png|200px]]||0.034
|-
|}

===References===
<references/>

File:AYK Maleic anhydrideLUMO.png

2010-12-17T15:59:08Z

Ayl08:

Rep:Module3:AYKLeung

2010-12-17T15:58:15Z

Ayl08: /* Cycloaddition between Cis-Butadiene and Ethylene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
!Molecule!! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||[[image:AYK_Cis-butadieneLUMO.png|200px]]||0.01707
|-
|Ethylene|| ||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====
AYK_Maleic_anhydrideHOMO.png

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T15:57:50Z

Ayl08: /* Cycloaddition between Maleic Anhydride with Cyclohexadiene */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||[[image:AYK_Cis-butadieneLUMO.png|200px]]||0.01707
|-
|Ethylene|| ||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====
AYK_Maleic_anhydrideHOMO.png

===References===
<references/>

File:AYK Maleic anhydrideHOMO.png

2010-12-17T15:57:39Z

Ayl08:

Rep:Module3:AYKLeung

2010-12-17T15:56:53Z

Ayl08: /* The Cope Rearrangement */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer<ref>B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, Mol. Phys., 2002, 100, 441[http://www.informaworld.com/smpp/content~db=all?content=10.1080/00268970110081412]</ref>. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||[[image:AYK_Cis-butadieneLUMO.png|200px]]||0.01707
|-
|Ethylene|| ||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T15:56:24Z

Ayl08: /* The Diels-Alder Cycloaddition */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
====Cycloaddition between Cis-Butadiene and Ethylene====
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||[[image:AYK_Cis-butadieneLUMO.png|200px]]||0.01707
|-
|Ethylene|| ||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

====Cycloaddition between Maleic Anhydride with Cyclohexadiene====

===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T15:54:27Z

Ayl08: /* The Cope Rearrangement */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||-234.559704
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||[[image:AYK_Cis-butadieneLUMO.png|200px]]||0.01707
|-
|Ethylene|| ||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:
===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T15:53:27Z

Ayl08: /* The Cope Rearrangement */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||[[image:AYK_Cis-butadieneLUMO.png|200px]]||0.01707
|-
|Ethylene|| ||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:
===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T15:52:18Z

Ayl08: /* References */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Output files for the two molecules:

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||[[image:AYK_Cis-butadieneLUMO.png|200px]]||0.01707
|-
|Ethylene|| ||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:
===References===
<references/>

Rep:Module3:AYKLeung

2010-12-17T15:52:04Z

Ayl08: /* The Diels-Alder Cycloaddition */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Output files for the two molecules:

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||[[image:AYK_Cis-butadieneLUMO.png|200px]]||0.01707
|-
|Ethylene|| ||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:
===References===
</references>

Rep:Module3:AYKLeung

2010-12-17T14:18:12Z

Ayl08: /* The Diels-Alder Cycloaddition */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Output files for the two molecules:

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:AYK_Cis-butadieneHOMO.png|200px]]||-0.34380||[[image:AYK_Cis-butadieneLUMO.png|200px]]||0.01707
|-
|Ethylene|| ||[[image:AYK_EthyleneHOMO.png|200px]]||-0.38775||[[image:AYK_EthyleneLUMO.png|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

File:AYK Cis-butadieneLUMO.png

2010-12-17T14:17:13Z

Ayl08:

File:AYK Cis-butadieneHOMO.png

2010-12-17T14:16:59Z

Ayl08:

File:AYK EthyleneLUMO.png

2010-12-17T14:09:55Z

Ayl08:

File:AYK EthyleneHOMO.png

2010-12-17T14:09:45Z

Ayl08:

Rep:Module3:AYKLeung

2010-12-17T13:43:06Z

Ayl08: /* The Diels-Alder Cycloaddition */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Output files for the two molecules:

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:|200px]]||-0.34380||[[image:200px]]||0.01707
|-
|Ethylene|| ||[[image:|200px]]||-0.38775||[[image:|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

Rep:Module3:AYKLeung

2010-12-17T13:42:58Z

Ayl08: /* The Diels-Alder Cycloaddition */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Output files for the two molecules:

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
[[Image: AYK_Diels_alder_mech.png|thumb|Diels-Alder Cycloaddition mechanism]]

In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|Thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:|200px]]||-0.34380||[[image:200px]]||0.01707
|-
|Ethylene|| ||[[image:|200px]]||-0.38775||[[image:|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

Rep:Module3:AYKLeung

2010-12-17T13:42:37Z

Ayl08: /* The Diels-Alder Cycloaddition */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Output files for the two molecules:

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
[[Image: AYK_Diels_alder_mech.png|Thumb|Diels-Alder Cycloaddition mechanism]]
In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:AYK_Synchronous&asynchronous.png|Thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:|200px]]||-0.34380||[[image:200px]]||0.01707
|-
|Ethylene|| ||[[image:|200px]]||-0.38775||[[image:|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

File:AYK Synchronous&asynchronous.png

2010-12-17T13:38:10Z

Ayl08:

File:AYK Diels alder mech.png

2010-12-17T13:35:58Z

Ayl08:

Rep:Module3:AYKLeung

2010-12-17T13:26:12Z

Ayl08: /* Optimising "Chair" and "Boat" Transition Structures */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Output files for the two molecules:

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC||25 ||47
|-
|IRC energy pathway & RMS Gradient||[[image:AYK_Single_step_IRC_Graphs.png|thumb]] ||[[image:AYK_Multiple_step_IRC_Graphs.png|thumb]]
|-
|Structure|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Single_step_IRC.mol2</uploadedFileContents>
<text>Single step Stucture</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Multiple_step_IRC.mol2</uploadedFileContents>
<text>Multiple step Stucture</text>
</jmolAppletButton>
</jmol>
|-
|Energy/a.u.||-231.688635 ||-231.691664
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
[[Image: |Thumb|Diels-Alder Cycloaddition mechanism]]
In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:|Thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:|200px]]||-0.34380||[[image:200px]]||0.01707
|-
|Ethylene|| ||[[image:|200px]]||-0.38775||[[image:|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

File:AYK Single step IRC.mol2

2010-12-17T13:25:49Z

Ayl08:

File:AYK Multiple step IRC.mol2

2010-12-17T13:24:45Z

Ayl08:

File:AYK Multiple step IRC Graphs.png

2010-12-17T13:21:48Z

Ayl08:

File:AYK Single step IRC Graphs.png

2010-12-17T13:18:26Z

Ayl08:

Rep:Module3:AYKLeung

2010-12-17T13:11:13Z

Ayl08: /* Optimising "Chair" and "Boat" Transition Structures */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Output files for the two molecules:

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at multiple steps
|-
|Points on IRC|| ||
|-
|IRC energy pathway|| ||
|-
|RMS Gradient|| ||
|-
|Structure|| ||
|-
|Energy/a.u.|| ||
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
[[Image: |Thumb|Diels-Alder Cycloaddition mechanism]]
In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:|Thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:|200px]]||-0.34380||[[image:200px]]||0.01707
|-
|Ethylene|| ||[[image:|200px]]||-0.38775||[[image:|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

Rep:Module3:AYKLeung

2010-12-17T13:10:43Z

Ayl08: /* Optimising "Chair" and "Boat" Transition Structures */

=Chemistry Computational Lab (Year 3)=
==Module 3: Transition States and Reactivity==
[http://www.cyberchem.com/gaussview.htm Gaussview 5] & [http://www.gaussian.com/g_prod/g09.htm Gaussian09] was used in all modelling exercises.
===The Cope Rearrangement===
[[image:AYK_Coperearrangement.png|thumb|Cope rearrangement mechanism for 1,5-hexadiene]]
[[image:AYK_Anti2Summary.png|thumb|left|200px|HF/3-21G summary table of anti2]]
The proposed Cope rearrangement mechanism of 1,5-hexadiene is shown on the right. It has a cyclic transition state in between. To find the preferred reaction mechanism low energy minima and transition state structures must be considered.

A molecule of 1,5-hexadiene with anti linkage at the centre 4 carbons was created and optimised under the conditions of HF/3-21G. This formation belongs to Ci point group. The energy was found to be the same as that of anti2 as stated in Appendix 1.

Another molecule of 1,5-hexadiene with gauche linkage was made and optimised with the methods same as above. The point group was found to be C1. Comparing the results with Appendix 1, the structure is identified as gauche3.
[[image:AYK_Gauche3Summary.png|thumb|Left|200px|HF/3-21G summary table of gauche3]]

With direct comparison between the 2 conformers, gauche3 would be expected to be the less stable molecule due to steric hindrance between the double bonds. But the results show the opposite, with the energy for gauche3 (a.u.) is lower than that of anti1 (a.u.). This could be explained by the orbital overlaps at where the π orbital of C=C interacts with the σ* orbital of the adjacent C-H bond, which stabilises the gauche molecule.

We have to consider both sterically and stereoelectronically, as mentioned above, therefore gauche3 is expected to be the most stable conformer. Other conformers were produced and optimised to compare with each other.

{| class="wikitable" border="1"
|+ ''Table 1: Summary of the optimised gauche and anti structures of 1,5-hexadiene"
! width="150"| Conformer !! width="100"| Energy (Hartree a.u.) !! width="100"| Point Group !! Summary tables||D-space files||Jmol
|- align="center"
| '''''anti2'''''||-231.69253525 || Ci ||[[image:AYK_Anti2Summary.png|thumb]]||{{DOI|10042/to-6275}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Ant2.mol</uploadedFileContents>
<text>Anti2</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche3'''''|| -231.69266122 || C1 || [[image:AYK_Gauche3Summary.png|thumb]]||{{DOI|10042/to-6273}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche3.mol</uploadedFileContents>
<text>Gauche3</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''anti1'''''||-231.692260237 || C2 || [[image:AYK_Anti1Summary.png|thumb]]||{{DOI|10042/to-6277}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Anti1.mol</uploadedFileContents>
<text>Anti1</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche4'''''|| -231.69153533|| C2 || [[image:AYK_Gauche4Summary.png|thumb]]||{{DOI|10042/to-6272}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche4.mol</uploadedFileContents>
<text>Gauche4</text>
</jmolAppletButton>
</jmol>
|- align="center"
| '''''gauche2'''''|| -231.69166702 || C2 || [[image:AYK_Gauche2Summary.png|thumb]]||{{DOI|10042/to-6271}}||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Gauche2.mol</uploadedFileContents>
<text>Gauche2</text>
</jmolAppletButton>
</jmol>
|}
The energies of different temperatures have very small differences
So it is shown that the gauche3 possesses the lowest energy among all.

The Ci anti2 conformer was created and optimised (shown above) using the HF/3-21G method.

This molecule is then reoptimised with another basis set (DFT/B3LYP/6-31G*) which is a more accurate method. Comparisons are made between the 2 sets of results (3-21G and 6-21G*) in the table below.

{| class="wikitable" border="1"
|+ ''Table 2: Summary of the optimised anti2 structures of 1,5-hexadiene with different basis sets"
! Molecule !! [[image:AYK_Anti2.png|thumb]] !! [[image:AYK_Anti2.png|thumb]]
|- align="center"
| Basis set ||HF/3-21G || B3LYP/6-31G*
|- align="center"
| File Type || .log || .log
|- align="center"
| Calculation Type || FOPT || FOPT
|- align="center"
| Calculation Method|| RHF || RB3LYP
|- align="center"
| Final Energy / Hartree a.u.|| -231.69253525 || -234.55970425
|- align="center"
| RMS Gradient Norm / a.u.|| 0.00002544 || 0.00004599
|- align="center"
| Dipole Moment / Debye || 0.000 || 0.000
|- align="center"
| Point Group|| C1|| C1
|}

The geometry of the compounds have not changed much but there is a difference in energies of the two different calculation method. The 6-31G* method gives an energy which is lower by about 3 a.u. and a lower RMS Norm. This shows that the 6-31G is better at optimising compounds to lower energies. The table
below shows the geometric data obtained from the 2 differently optimised compounds.

{| class="wikitable" border="1"
|+ Table 3: Geometric properties of 2 differently optimised (anti2) 1,5-hexadiene
! !! Colspan="3"| Dihedral Angle (o) !! Colspan="3"| Bond Length (Å)
|-
!Basis set!! C2-C3-C4-C5!!C1-C2-C3-C4!!C3-C4-C5-C6!!C1-C2 & C5-C6!!C2-C3 & C4-C5!!C3-C4
|-align="Center"
|'''HF 3-21G''||180.0 ||118.8 || 118.8||1.32 ||1.51 ||1.55
|-align="center"
|''B3LYP 6-31G*''||180.0 || 118.8|| 118.8 ||1.32||1.51 ||1.55
|}
There is not a large difference between the geometric values two differently optimised compounds. Bond lengths differ by 0.01 Å at parts. Comparing with the lit. values (C=C 1.34Å, C-C 1.54Å, both simulations give good agreements.

Output files for the two molecules:

Frequency analysis was carried out using the anti2 conformer, under 6-31G* optimisation.
The IR spectrum of this compound is shown on the right.
[[image:AYK_Anti2reoptSpectrum.png |thumb|Anti2 structure vibrational spectrum]]
File on D-space: {{DOI|10042/to-6276}}
No imaginary frequencies were observed and this means it is optimised to its minimum.

Another analysis was carried out at 0K, and the results are shown below.
{| class="wikitable" border="1"
|+ ''Table 4: Thermochemical data from frequency analysis of optimised anti2 structures of 1,5-hexadiene with 6-31G* at different temperatures''
! !! 298.15K!!0K
|-
|Final Energies (Eh)|| -234.559704||
|-
|Sum of electronic and zero-point energies (Eh)|| -234.416244||-234.416244
|-
|Sum of electronic and thermal energies (Eh)||-234.408954 ||-234.408370
|-
|Sum of electron and thermal enthalpies (Eh)||-234.408010 ||-234.406438
|-
|Sum of electronic and free energies (Eh) ||-234.447849 ||-234.447398
|}

The energies do not differ by a lot, and in general the energy of the compound at 0K is less negative than that at 298.15K. This might be because the energies at a lower temperature hinders electronic movements.

===Optimising "Chair" and "Boat" Transition Structures===
[[image:AYK_Allyl_fragment.png|thumb|Single allyl fragment]]
[[image:AYL_Allyls_in_Chair_TS.png|thumb|Proposed TS structure]]

In this experiment and "chair" and "boat" transition structures of the Cope rearrangement are looked at and compared against each other.

An allyl fragment (CH2CHCH2) was created and optimised under the method of HK/3-21G. A transition state could also be hypothesised. The diagrams below shows the allyl fragment and the proposed Transition State (TS) structure.

Optimisation and frequency analysis of the TS structure was carried out under the HF/3-21G basis set. An imaginary frequency at 818cm-1 was observed at the results. The animation also proves that this corresponds to the Cope arrangement.

A same calculation is carried out with ModRedundant Minimisation with frozen C-C bond lengths fixed at 2.20Å. Now the imaginary frequency is.

The table below shows the results obtained in the two simulations.

{| class="wikitable" border="1"
|+ ''Table 5: Results obtained for different optimisation methods at TS''
! !! TS (Berny) !! Redundant Coordinate
|-
|Allyl C-C bond length|| 2.021||2.200
|-
|Final Energy (Hartree a.u.)||-231.619322 ||-231.614023
|-
|RMS Gradient (a.u.)||0.00005006 ||0.006031
|-
|Dipole Moment (Debye)|| 0.0017||0.0103
|-
|Point Group ||C2h ||C2h
|-
|Imaginary Vibration Frequency (cm-1)||-818 ||-672.
|-
|Jmol|| <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSBerny.mol2</uploadedFileContents>
<text>TSBerny optimised</text>
</jmolAppletButton>
</jmol>||<jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_TSRCoptimised.mol2</uploadedFileContents>
<text>TS Redundant Coordinate </text>
</jmolAppletButton>
</jmol>
|}

As for the Boat structure, a new method (QST2) was introduced to optimise the compound, which takes the coordinates of the reactants and products into account of the calculation. The Opt+freq job was done with a basis set of HF/3-21G. The outcome was a failure because the reactant and product were too similar and that it could not give the correct transition state geometry. See diagram for the failed optimisation.

[[image:AYK_Unsuccessful_QST2_optimisation_of_Boat_structure.png|centre|250px|Unsuccessful QST2 optimisation of Boat structure]]
Jmol of failed TS: <jmol>
<jmolAppletButton>
<uploadedFileContents>AYK_Failed_TS.mol2</uploadedFileContents>
<text>Unsuccessful TS (boat)</text>
</jmolAppletButton>
</jmol>

We cannot deduce the geometry of the final product of the reaction between 2 allyl fragments even though both transition state geometries of the boat and chair conformers were obtained. The Intrinsic Reaction Coordinate (IRC) was introduced to calculate the model and this method follows the minimum energy path from a transition structure down its local minimum energy path. This method is applied in two ways: once with only one calculation, the other with calculations at every single step. The second method provides a more accurate result, shown by the lower total energy value by 0.0 a.u. and that the IRC energy curve is closer to the minimum.

From the energy and the point group of the final structure, we may conclude that the chair TS leads to a formation of the Gouche2 conformer, as shown in Appendix2.

{| class="wikitable" border="1"
|+ ''Table 6: Summaries obtained for two IRC optimisation methods at the Chair TS''
! !! Single Calculation !! Calculations at every step
|-
|Points on IRC|| ||
|-
|IRC energy pathway|| ||
|-
|RMS Gradient|| ||
|-
|Structure|| ||
|-
|Energy/a.u.|| ||
|-
|Point Group||C2 ||C2
|-
|}
These compounds do not geometrically differ a lot, but as the every step method produces a lower energy, it is believed to be a more accurate method.

In order to compare results between basis sets and boat & chair TS at different temperatures, (@298.15 and 0K)
{| class="wikitable" border="1"
|+ ''Table 7: Summary for the chair and boat transition structures under different temperatures and methods''
! !! colspan="3"|HF/3-21G !! colspan="3"|B3LYP/6-31G*
|-
| ||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)||Electronic energy (a.u.) ||Sum of electronic and zero-point energies @0K (a.u.) ||Sum of electronic and thermal energies @298.15K (a.u.)
|-
|Chair TS|| -231.619322||-231.466345||-231.461344||-234.556983||-234.414599||-234.409001
|-
|Boat TS|| -231.602802||-231.450586||-231.445302||-234.543093||-234.402063||-234.396007
|-
|Reactant Anti2||-231.692535||-231.539170||-234.559704||-234.611705||-234.468904||-234.461875
|-
|}
With the data in the table above, the activation energy of the boat and chair TS reactions could be worked out, shown in the table below:

{|Class="wikitable" border="1"
|+ "Table 8: Summary of activation energies"
! !!colspan="2"|HF/3-21G !! colspan="2"|B3LYP/6-31G*||Expt.
|-
| ||@0K||@298.15K||@0K||@298.15K||@0K
|-
|Chair TS ΔE||45.70||44.69||34.08||33.18||33.5 ±0.05
|-
|Boat TS ΔE||55.59||54.76||41.94||41.33||44.7 ±2.0
|-
|}
The Activation Energies agree with the lit. values at 0K. Since for all temperatures the chair TS ΔE is always lower than that of the boat TS, the chair structure should be the preferred pathway of this reaction.

===The Diels-Alder Cycloaddition===
[[Image: |Thumb|Diels-Alder Cycloaddition mechanism]]
In this part we are investigating the Diels-Alder cycloaddition of butadiene and ethylene. Mechanism of reaction shown in diagram on the right. The molecular orbitals of the reactants and the transition state are looked at.
[[image:|Thumb|Diels-Alder synchronous and asynchronous pathways]]
There are two ways of how the reaction transition state could go, synchronous or asynchronous, i.e. either concerted: bond broken then formation, or vice versa. They are shown in the diagram on the right.

Firstly the cis-butadiene and ethylene were created and optimised using the AM1 semi-empirical molecular orbital method. The interacting molecular orbitals of the reactants are shown below.
{| class="wikitable" border="1"
|+ ''Table 8: HOMO & LUMOs of cis-butadiene & ethylene and their energies ''
! !! Structure !! HOMO!! HOMO energy (a.u.)!!LUMO!!LUMO energy (a.u.)
|-
|Cis-butadiene|| ||[[image:|200px]]||-0.34380||[[image:200px]]||0.01707
|-
|Ethylene|| ||[[image:|200px]]||-0.38775||[[image:|200px]]||0.05284
|-
|}
By observing the shapes of the orbitals one would expect the HOMO of the cis-butadiene to react with the LUMO of the ethylene. Also looking at the energy differences between the HOMO-LUMO it is also shown that the HOMO@Butadiene-LUMO@Ethylene has a smaller difference than the other way round. This agrees well with the assumption that cis-butadiene acts as an electron acceptor, with the ethylene being the donor.

The QST2 method was chosen over the TS(Berny) method to investigate the transition state of this experiment due to the accuracy and reasons discussed above. The geometry data of the TS is shown below.

{| class="wikitable" border="1"
|+ ''Table 9: Bond lengths during TS of cis-butadiene & ethylene ''
! Carbon-Carbon bond!!Bond Length (Å)
|-
|
|-
|
|-
|
|-
|
|-
|Csp3-Csp3||1.53
|-
|Csp2-Csp2||1.48
|-
|}

Typical values of carbon carbon bonds are also shown for comparison. They are different from the calculated results because the whole system is conjucated to a certain extent. The lengths of the newly-formed bonds are longer than a typical C-C bond and/or a typical Van der Waals radius (1.70Å).

[[image:]]
The imaginary vibration of this transition state is found to be at -956cm-1, which indicates the bond formation. The animation of this vibration shows that the vibration is synchronous, i.e. concerted reaction.

By looking at the HOMO and LUMO at the transition states we could see that they correspond to the HOMOs and LUMOs of the reactants. The HOMO is the interaction between HOMO@Butadiene and LUMO@Ethylene, and the LUMO shows characteristics of HOMO@Ethylene and LUMO@Butadiene.

The TS system was reoptimised using another basis set: DFT/B3LYP/6-31G, and the data of two optimisations are shown below:

File:AYK Successful TS.mol2

2010-12-17T13:03:42Z

Ayl08: