ChemWiki - User contributions [en]

Rep:Mod:smb59mod3

2012-02-20T16:58:40Z

Sb5009:

Two different types of transition states are studied. Firstly the two possible transition states of the cope rearrangement of 1,5-hexadiene and the various optimised conformers the final molecule can form are analysed and compared to literature values. The second reaction studied is the diels-alder reaction, where the formation of the transition state and the stabilising effect of secondary orbital overlap are shown to result in a reaction based of kinetics.

==Cope rearrangement==

===1,5-hexadiene===

[[file:sbmod3HM.png|center]]
The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above<ref>Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G, with both undergoing a frequency analysis to ensure the stationary point reached was a minimum.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 DFT B3LYP frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

===Transition states===
====Boat structure====
Following this, the chair and boat transition states were calculated using different methods. First, to form the chair transition state, two optimised (HF/3-21G) allyl fragments were placed (CH<sub>2</sub>CHCH<sub>2</sub>) approximating a hexane chair structure with the carbons with C<sub>2h</sub> symmetry. This was then optimised to a TS (berny), giving a single vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CV1.gif -818cm<sup>-1</sup>]<ref>[[file:Sbmod3CL1.LOG]]</ref>. Afterwards, a second method was used, via freezing the bond length between the reacting carbons to 2.2 angstroms, minimising using HF/3-21G, then minimising to a TS (berny) after setting the frozen bonds to derivative, giving a transitional vibration at -818cm<sup>-1</sup><ref>[[file:Sbmod3CL2B.LOG]]</ref> again, but with 2.0199 angstroms seperating the reacting carbons (Decreasing from 2.0206).
====Chair structure====
To form the C<sub>2v</sub> boat structure, the transition state was found using QST2, first using ther anti2 molecule above and renumbering the atoms to simulate the molecule before and after the transition. However, this failed initially due to the shape of anti2 <ref>[[file:Sbmod3CL1.LOG]]</ref>. This was improved upon by changing the inner dihedral angle to 0 and the inside carbon angles to 100', resulting in molecules similar to just before and after a transition. This resulted in a successful transition state formed, with a transition vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3BT.gif -840cm<sup>-1</sup>]<ref>[[file:Sbmod3CL2.LOG]]</ref>. An additional attempt to use the initial Anti2 molecules was successful by using QST3, which involves aiding the calculation by adding an approximated transition state. This lead to a near identical transition state at -840cm<sup>-1</sup><ref>http://hdl.handle.net/10042/to-12703</ref>

To demonstrate what occurs after the transition state, an IRC was performed (100 steps, force constants calculated each time, with final molecule optimised again, all using HF as above), demonstrating that the chair transition state ended forming the guache2<ref>http://hdl.handle.net/10042/to-12717</ref><ref>http://hdl.handle.net/10042/to-12718</ref> ([https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CIRC.gif view])product above after the transition step, while the boat initially formed gauche2, but subsequently minimised to form gauche3<ref>http://hdl.handle.net/10042/to-12715</ref><ref>http://hdl.handle.net/10042/to-12716</ref> ([https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3BIRC.gif view])

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti2 and transition state energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>http://hdl.handle.net/10042/to-12708</ref>
| -231.539540<ref>http://hdl.handle.net/10042/to-12708</ref>
| style="border-right: 2px solid grey;" | -231.532566<ref>http://hdl.handle.net/10042/to-12708</ref>
| -234.611710<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.469204<ref>http://hdl.handle.net/10042/to-12706</ref>
| -234.461857<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.444170<ref>http://hdl.handle.net/10042/to-12707</ref>
|- style="text-align: center;"
! Chair
| -231.619322<ref>[[File:Sbmod3CL2B.LOG]]</ref>
| -231.466696<ref[[>File:Sbmod3CL2B.LOG]]</ref>
|style="border-right: 2px solid grey;" | -231.461337<ref>[[File:Sbmod3CL2B.LOG]]</ref>
| -234.556981<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.414906<ref>http://hdl.handle.net/10042/to-12712</ref>
| -234.408982<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.392032<ref>http://hdl.handle.net/10042/to-12714</ref>
|- style="text-align: center;"
! Boat
| -231.602802<ref>[[File:Sbmod3BL2.LOG]]</ref>
| -231.450928<ref>[[File:Sbmod3BL2.LOG]]</ref>
|style="border-right: 2px solid grey;" | -231.445299 <ref>[[File:Sbmod3BL2.LOG]]</ref>
| -234.543093<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.402339<ref>http://hdl.handle.net/10042/to-12710</ref>
| -234.396005<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.378575<ref>http://hdl.handle.net/10042/to-12711</ref>
|}

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Transition energies relative to Anti2 (in kcal/mol)
|-
!
! colspan=2 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=3 style="border-right: 2px solid grey;" | DFT/6-31G*
! Expt.
|-
! State
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

600k
! 0k
|- style="text-align: center;"
! Chair
| 45.71
|style="border-right: 2px solid grey;" |44.70
| 34.07
| 33.18
| style="border-right: 2px solid grey;" | 32.72
| 33.5 ± 0.5
|- style="text-align: center;"
! Boat
| 55.60
|style="border-right: 2px solid grey;" |54.76
| 41.96
| 41.32
| style="border-right: 2px solid grey;" | 41.16
| 44.7 ± 2.0
|}

Both sets of calculations show that the chair transition structure is ~10kcal/mol lower in energy than the boat (as expected if compared to hexane structures) transition, however the second optimisation values are significantly closer to the experimental results. This demonstrates the greater accuracy of the DFT method over the HF optimisation. The DFT versions ~1kcal/mol out compared to the range of the experimental. This shows the calculations were done correctly, and demonstrates the accuracy of the DFT method.

==Diels-alder==

[[file:Sbmod3DAM.png|center]]
The diels-alder reaction is a cyclic addition of a alkene group to a cis conjugated diene as above. The alkene approaches and the reaction occurs due to strong orbital overlap viewable below.

To analyse this reaction, the transition state had to be predicted. This was done, as described above, by freezing the reacting bond distance at 2.2 angstroms, optimising, then optimising to a transition state with the reacting bonds set to derivative<ref>http://hdl.handle.net/10042/to-12719</ref>. The resulting transition structure shows a distinct negative synchronous vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3DAT.gif -957cm<sup>-1</sup>], confirming its nature as a transition state for the diels alder reaction. The transition state forming C-C bonds are 2.118<ref>http://hdl.handle.net/10042/to-12719</ref> angstroms long, which collapse to 1.519<ref>http://hdl.handle.net/10042/to-12720</ref> angstroms after a minimisation. In the
<jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DATS.mol</uploadedFileContents>
<text>'''transition state'''</text>
<script>background=black; measure 1 11; measure 14 8; measure 11 14; measure 1 4; measure 4 6; measure 6 8</script>
</jmolAppletLink>
</jmol>
the butadiene segment shows bond lengths (0.138-0.140nm) similar to benzene (0.14nm) This is due to the electron donation from the butadiene HOMO into the ethene LUMO, and the ethene HOMO into the butadiene LUMO. This results in a decrease in bond order between the alkene bonds (normally 0.134nm) and an increase in the bond order for the sp2 C-C butadiene bond due to the shape of the LUMO as below.

The table below shows the HOMO-LUMO orbitals of the molecules involves. They clearly show the HOMO of the transition state is the result of the ethene LUMO and the butadiene HOMO, which all share a symmetry, whilst the LUMO is formed from the thene HOMO and the butadiene LUMO, which share s symmetry.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+Orbitals
! molecule
! HOMO
(symmetry)
!LUMO
(symmetry)
|-
!rowspan=2|Butadiene<ref>http://hdl.handle.net/10042/to-12721</ref>
|[[file:Sbmod3BH.png|300px]]
|[[file:Sbmod3BL.png|300px]]
|-style="text-align: center;"
|a
|s
|-
!rowspan=2|Ethene<ref>http://hdl.handle.net/10042/to-12726</ref>
|[[file:Sbmod3EH.png|300px]]
|[[file:Sbmod3LH.png|300px]]
|-style="text-align: center;"
|s
|a
|-
!rowspan=2|Cyclohexene TS<ref>http://hdl.handle.net/10042/to-12719</ref>
|[[file:Sbmod3DATSH.png|300px]]
|[[file:Sbmod3DATSL.png|300px]]
|-style="text-align: center;"
|a
|s
|}

{| class="wikitable"; border="0"; style="margin: 1em auto 1em auto;"
|-style="text-align: center;"
|Endo
|width="200" |
|Exo
|-
|[[file:Sbmod3DAEnM.png|center]]
|
|[[file:Sbmod3DAExM.png|center]]
|-style="text-align: center;"
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3DAEnT.gif -810cm<sup>-1</sup>]
|
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3DAExT.gif -814cm<sup>-1</sup>]
|}

After examining the basic Diels alder reaction, the above more complex version involving stereochemistry was subsequently analysed. In this reaction, the orientation of the attack determines the subsequent transition state and final molecule. This was done in an attempt to determine which product would be the kinetic and thermodynamic product. After starting with AM1 optimised starting reactants, the transition state for each orientation was found as above using the freeze and derivative method. After acquiring the AM1 transition states, they were further refined using the PM6 optimisation method. Using these transition states, an IRC was run to find the energy of the final products.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ energy comparison
|-
!
! colspan=3 style="border-right: 2px solid grey;" | AM1
! colspan=3 | PM6
|-
! Molecule
! Electronic energy
! New C-C length
! style="border-right: 2px solid grey;" | Through space
C-C length
! Electronic energy
! New C-C length
! Through space
C-C length
|-
! <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3Endots.mol</uploadedFileContents>
<text>Endo TS</text>
<script>background=black</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12727</ref><ref>http://hdl.handle.net/10042/to-12729</ref>
| -0.05121220
| 2.14913
|style="border-right: 2px solid grey;" | 2.85929
| -0.06243761
| 2.14913
| 2.85843
|-
! <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3Exots.mol</uploadedFileContents>
<text>Exo TS</text>
<script>background=black</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12728</ref><ref>http://hdl.handle.net/10042/to-12730</ref>
| -0.05027834
| 2.16151
|style="border-right: 2px solid grey;" | 2.93695
| -0.05981691
| 2.16377
| 2.93486
|-
! <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3Endo.mol</uploadedFileContents>
<text>Endo</text>
<script>background=black</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12727</ref><ref>http://hdl.handle.net/10042/to-12729</ref>
| -0.16017041
| 1.53587
|style="border-right: 2px solid grey;" | 2.98378
| -0.17125794
| 1.55749
| 2.92347
|-
! <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3Exo.mol</uploadedFileContents>
<text>Exo</text>
<script>background=black</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12728</ref><ref>http://hdl.handle.net/10042/to-12730</ref>

| -0.15990940
| 1.53608
|style="border-right: 2px solid grey;" | 2.94318
| -0.17163675
| 1.55678
| 2.95734
|}

The PM6 shows that the endo product is preferred kinetically due to the lower energy transition state, but the exo product has a lower final product and so is preferred thermodynamically. The noticable narrower endo transition state C C through space indicates secondary orbital overlap<ref>

Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet

J. Org. Chem., 1987, 52 (8), pp 1469–1474

DOI: 10.1021/jo00384a016

Publication Date: April 1987

</ref>, viewable in LUMO2 + LUMO3 below, but absent in both the final product and both the exo transition state and final form. This stabilising interaction would explain the lower energy endo transition state and why it would be the preferred product.

{| class="wikitable"; border="0"; style="margin: 1em auto 1em auto;"
|-style="text-align: center;"
|LUMO+1
|width="200" |
|LUMO+2
|-
|[[file:Sbmod3DAEnL2.png|450px]]
|
|[[file:Sbmod3DAEnL3.png|400px]]
|}

<references/>

Rep:Mod:smb59mod3

2012-02-20T16:54:29Z

Sb5009:

==Cope rearrangement==

===1,5-hexadiene===

[[file:sbmod3HM.png|center]]
The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above<ref>Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G, with both undergoing a frequency analysis to ensure the stationary point reached was a minimum.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 DFT B3LYP frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

===Transition states===
====Boat structure====
Following this, the chair and boat transition states were calculated using different methods. First, to form the chair transition state, two optimised (HF/3-21G) allyl fragments were placed (CH<sub>2</sub>CHCH<sub>2</sub>) approximating a hexane chair structure with the carbons with C<sub>2h</sub> symmetry. This was then optimised to a TS (berny), giving a single vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CV1.gif -818cm<sup>-1</sup>]<ref>[[file:Sbmod3CL1.LOG]]</ref>. Afterwards, a second method was used, via freezing the bond length between the reacting carbons to 2.2 angstroms, minimising using HF/3-21G, then minimising to a TS (berny) after setting the frozen bonds to derivative, giving a transitional vibration at -818cm<sup>-1</sup><ref>[[file:Sbmod3CL2B.LOG]]</ref> again, but with 2.0199 angstroms seperating the reacting carbons (Decreasing from 2.0206).
====Chair structure====
To form the C<sub>2v</sub> boat structure, the transition state was found using QST2, first using ther anti2 molecule above and renumbering the atoms to simulate the molecule before and after the transition. However, this failed initially due to the shape of anti2 <ref>[[file:Sbmod3CL1.LOG]]</ref>. This was improved upon by changing the inner dihedral angle to 0 and the inside carbon angles to 100', resulting in molecules similar to just before and after a transition. This resulted in a successful transition state formed, with a transition vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3BT.gif -840cm<sup>-1</sup>]<ref>[[file:Sbmod3CL2.LOG]]</ref>. An additional attempt to use the initial Anti2 molecules was successful by using QST3, which involves aiding the calculation by adding an approximated transition state. This lead to a near identical transition state at -840cm<sup>-1</sup><ref>http://hdl.handle.net/10042/to-12703</ref>

To demonstrate what occurs after the transition state, an IRC was performed (100 steps, force constants calculated each time, with final molecule optimised again, all using HF as above), demonstrating that the chair transition state ended forming the guache2<ref>http://hdl.handle.net/10042/to-12717</ref><ref>http://hdl.handle.net/10042/to-12718</ref> ([https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CIRC.gif view])product above after the transition step, while the boat initially formed gauche2, but subsequently minimised to form gauche3<ref>http://hdl.handle.net/10042/to-12715</ref><ref>http://hdl.handle.net/10042/to-12716</ref> ([https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3BIRC.gif view])

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti2 and transition state energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>http://hdl.handle.net/10042/to-12708</ref>
| -231.539540<ref>http://hdl.handle.net/10042/to-12708</ref>
| style="border-right: 2px solid grey;" | -231.532566<ref>http://hdl.handle.net/10042/to-12708</ref>
| -234.611710<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.469204<ref>http://hdl.handle.net/10042/to-12706</ref>
| -234.461857<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.444170<ref>http://hdl.handle.net/10042/to-12707</ref>
|- style="text-align: center;"
! Chair
| -231.619322<ref>[[File:Sbmod3CL2B.LOG]]</ref>
| -231.466696<ref[[>File:Sbmod3CL2B.LOG]]</ref>
|style="border-right: 2px solid grey;" | -231.461337<ref>[[File:Sbmod3CL2B.LOG]]</ref>
| -234.556981<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.414906<ref>http://hdl.handle.net/10042/to-12712</ref>
| -234.408982<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.392032<ref>http://hdl.handle.net/10042/to-12714</ref>
|- style="text-align: center;"
! Boat
| -231.602802<ref>[[File:Sbmod3BL2.LOG]]</ref>
| -231.450928<ref>[[File:Sbmod3BL2.LOG]]</ref>
|style="border-right: 2px solid grey;" | -231.445299 <ref>[[File:Sbmod3BL2.LOG]]</ref>
| -234.543093<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.402339<ref>http://hdl.handle.net/10042/to-12710</ref>
| -234.396005<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.378575<ref>http://hdl.handle.net/10042/to-12711</ref>
|}

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Transition energies relative to Anti2 (in kcal/mol)
|-
!
! colspan=2 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=3 style="border-right: 2px solid grey;" | DFT/6-31G*
! Expt.
|-
! State
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

600k
! 0k
|- style="text-align: center;"
! Chair
| 45.71
|style="border-right: 2px solid grey;" |44.70
| 34.07
| 33.18
| style="border-right: 2px solid grey;" | 32.72
| 33.5 ± 0.5
|- style="text-align: center;"
! Boat
| 55.60
|style="border-right: 2px solid grey;" |54.76
| 41.96
| 41.32
| style="border-right: 2px solid grey;" | 41.16
| 44.7 ± 2.0
|}

Both sets of calculations show that the chair transition structure is ~10kcal/mol lower in energy than the boat (as expected if compared to hexane structures) transition, however the second optimisation values are significantly closer to the experimental results. This demonstrates the greater accuracy of the DFT method over the HF optimisation. The DFT versions ~1kcal/mol out compared to the range of the experimental. This shows the calculations were done correctly, and demonstrates the accuracy of the DFT method.

==Diels-alder==

[[file:Sbmod3DAM.png|center]]
The diels-alder reaction is a cyclic addition of a alkene group to a cis conjugated diene as above. The alkene approaches and the reaction occurs due to strong orbital overlap viewable below.

To analyse this reaction, the transition state had to be predicted. This was done, as described above, by freezing the reacting bond distance at 2.2 angstroms, optimising, then optimising to a transition state with the reacting bonds set to derivative<ref>http://hdl.handle.net/10042/to-12719</ref>. The resulting transition structure shows a distinct negative synchronous vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3DAT.gif -957cm<sup>-1</sup>], confirming its nature as a transition state for the diels alder reaction. The transition state forming C-C bonds are 2.118<ref>http://hdl.handle.net/10042/to-12719</ref> angstroms long, which collapse to 1.519<ref>http://hdl.handle.net/10042/to-12720</ref> angstroms after a minimisation. In the
<jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DATS.mol</uploadedFileContents>
<text>'''transition state'''</text>
<script>background=black; measure 1 11; measure 14 8; measure 11 14; measure 1 4; measure 4 6; measure 6 8</script>
</jmolAppletLink>
</jmol>
the butadiene segment shows bond lengths (0.138-0.140nm) similar to benzene (0.14nm) This is due to the electron donation from the butadiene HOMO into the ethene LUMO, and the ethene HOMO into the butadiene LUMO. This results in a decrease in bond order between the alkene bonds (normally 0.134nm) and an increase in the bond order for the sp2 C-C butadiene bond due to the shape of the LUMO as below.

The table below shows the HOMO-LUMO orbitals of the molecules involves. They clearly show the HOMO of the transition state is the result of the ethene LUMO and the butadiene HOMO, which all share a symmetry, whilst the LUMO is formed from the thene HOMO and the butadiene LUMO, which share s symmetry.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+Orbitals
! molecule
! HOMO
(symmetry)
!LUMO
(symmetry)
|-
!rowspan=2|Butadiene<ref>http://hdl.handle.net/10042/to-12721</ref>
|[[file:Sbmod3BH.png|300px]]
|[[file:Sbmod3BL.png|300px]]
|-style="text-align: center;"
|a
|s
|-
!rowspan=2|Ethene<ref>http://hdl.handle.net/10042/to-12726</ref>
|[[file:Sbmod3EH.png|300px]]
|[[file:Sbmod3LH.png|300px]]
|-style="text-align: center;"
|s
|a
|-
!rowspan=2|Cyclohexene TS<ref>http://hdl.handle.net/10042/to-12719</ref>
|[[file:Sbmod3DATSH.png|300px]]
|[[file:Sbmod3DATSL.png|300px]]
|-style="text-align: center;"
|a
|s
|}

{| class="wikitable"; border="0"; style="margin: 1em auto 1em auto;"
|-style="text-align: center;"
|Endo
|width="200" |
|Exo
|-
|[[file:Sbmod3DAEnM.png|center]]
|
|[[file:Sbmod3DAExM.png|center]]
|-style="text-align: center;"
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3DAEnT.gif -810cm<sup>-1</sup>]
|
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3DAExT.gif -814cm<sup>-1</sup>]
|}

After examining the basic Diels alder reaction, the above more complex version involving stereochemistry was subsequently analysed. In this reaction, the orientation of the attack determines the subsequent transition state and final molecule. This was done in an attempt to determine which product would be the kinetic and thermodynamic product. After starting with AM1 optimised starting reactants, the transition state for each orientation was found as above using the freeze and derivative method. After acquiring the AM1 transition states, they were further refined using the PM6 optimisation method. Using these transition states, an IRC was run to find the energy of the final products.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ energy comparison
|-
!
! colspan=3 style="border-right: 2px solid grey;" | AM1
! colspan=3 | PM6
|-
! Molecule
! Electronic energy
! New C-C length
! style="border-right: 2px solid grey;" | Through space
C-C length
! Electronic energy
! New C-C length
! Through space
C-C length
|-
! <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3Endots.mol</uploadedFileContents>
<text>Endo TS</text>
<script>background=black</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12727</ref><ref>http://hdl.handle.net/10042/to-12729</ref>
| -0.05121220
| 2.14913
|style="border-right: 2px solid grey;" | 2.85929
| -0.06243761
| 2.14913
| 2.85843
|-
! <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3Exots.mol</uploadedFileContents>
<text>Exo TS</text>
<script>background=black</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12728</ref><ref>http://hdl.handle.net/10042/to-12730</ref>
| -0.05027834
| 2.16151
|style="border-right: 2px solid grey;" | 2.93695
| -0.05981691
| 2.16377
| 2.93486
|-
! <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3Endo.mol</uploadedFileContents>
<text>Endo</text>
<script>background=black</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12727</ref><ref>http://hdl.handle.net/10042/to-12729</ref>
| -0.16017041
| 1.53587
|style="border-right: 2px solid grey;" | 2.98378
| -0.17125794
| 1.55749
| 2.92347
|-
! <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3Exo.mol</uploadedFileContents>
<text>Exo</text>
<script>background=black</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12728</ref><ref>http://hdl.handle.net/10042/to-12730</ref>

| -0.15990940
| 1.53608
|style="border-right: 2px solid grey;" | 2.94318
| -0.17163675
| 1.55678
| 2.95734
|}

The PM6 shows that the endo product is preferred kinetically due to the lower energy transition state, but the exo product has a lower final product and so is preferred thermodynamically. The noticable narrower endo transition state C C through space indicates secondary orbital overlap<ref>

Marye Anne Fox, Raul Cardona, Nicoline J. Kiwiet

J. Org. Chem., 1987, 52 (8), pp 1469–1474

DOI: 10.1021/jo00384a016

Publication Date: April 1987

</ref>, viewable in LUMO2 + LUMO3 below, but absent in both the final product and both the exo transition state and final form. This stabilising interaction would explain the lower energy endo transition state and why it would be the preferred product.

{| class="wikitable"; border="0"; style="margin: 1em auto 1em auto;"
|-style="text-align: center;"
|LUMO+1
|width="200" |
|LUMO+2
|-
|[[file:Sbmod3DAEnL2.png|450px]]
|
|[[file:Sbmod3DAEnL3.png|400px]]
|}

<references/>

Rep:Mod:smb59mod3

2012-02-20T16:53:03Z

Sb5009:

==Cope rearrangement==

===1,5-hexadiene===

[[file:sbmod3HM.png|center]]
The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above<ref>Clayden, J.; Greeves, N.; Warren, S.; Wothers, P.; Organic Chemistry, 2011, Oxford University Press</ref>. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G, with both undergoing a frequency analysis to ensure the stationary point reached was a minimum.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 DFT B3LYP frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

===Transition states===
====Boat structure====
Following this, the chair and boat transition states were calculated using different methods. First, to form the chair transition state, two optimised (HF/3-21G) allyl fragments were placed (CH<sub>2</sub>CHCH<sub>2</sub>) approximating a hexane chair structure with the carbons with C<sub>2h</sub> symmetry. This was then optimised to a TS (berny), giving a single vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CV1.gif -818cm<sup>-1</sup>]<ref>[[file:Sbmod3CL1.LOG]]</ref>. Afterwards, a second method was used, via freezing the bond length between the reacting carbons to 2.2 angstroms, minimising using HF/3-21G, then minimising to a TS (berny) after setting the frozen bonds to derivative, giving a transitional vibration at -818cm<sup>-1</sup><ref>[[file:Sbmod3CL2B.LOG]]</ref> again, but with 2.0199 angstroms seperating the reacting carbons (Decreasing from 2.0206).
====Chair structure====
To form the C<sub>2v</sub> boat structure, the transition state was found using QST2, first using ther anti2 molecule above and renumbering the atoms to simulate the molecule before and after the transition. However, this failed initially due to the shape of anti2 <ref>[[file:Sbmod3CL1.LOG]]</ref>. This was improved upon by changing the inner dihedral angle to 0 and the inside carbon angles to 100', resulting in molecules similar to just before and after a transition. This resulted in a successful transition state formed, with a transition vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3BT.gif -840cm<sup>-1</sup>]<ref>[[file:Sbmod3CL2.LOG]]</ref>. An additional attempt to use the initial Anti2 molecules was successful by using QST3, which involves aiding the calculation by adding an approximated transition state. This lead to a near identical transition state at -840cm<sup>-1</sup><ref>http://hdl.handle.net/10042/to-12703</ref>

To demonstrate what occurs after the transition state, an IRC was performed (100 steps, force constants calculated each time, with final molecule optimised again, all using HF as above), demonstrating that the chair transition state ended forming the guache2<ref>http://hdl.handle.net/10042/to-12717</ref><ref>http://hdl.handle.net/10042/to-12718</ref> ([https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CIRC.gif view])product above after the transition step, while the boat initially formed gauche2, but subsequently minimised to form gauche3<ref>http://hdl.handle.net/10042/to-12715</ref><ref>http://hdl.handle.net/10042/to-12716</ref> ([https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3BIRC.gif view])

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti2 and transition state energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>http://hdl.handle.net/10042/to-12708</ref>
| -231.539540<ref>http://hdl.handle.net/10042/to-12708</ref>
| style="border-right: 2px solid grey;" | -231.532566<ref>http://hdl.handle.net/10042/to-12708</ref>
| -234.611710<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.469204<ref>http://hdl.handle.net/10042/to-12706</ref>
| -234.461857<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.444170<ref>http://hdl.handle.net/10042/to-12707</ref>
|- style="text-align: center;"
! Chair
| -231.619322<ref>[[File:Sbmod3CL2B.LOG]]</ref>
| -231.466696<ref[[>File:Sbmod3CL2B.LOG]]</ref>
|style="border-right: 2px solid grey;" | -231.461337<ref>[[File:Sbmod3CL2B.LOG]]</ref>
| -234.556981<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.414906<ref>http://hdl.handle.net/10042/to-12712</ref>
| -234.408982<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.392032<ref>http://hdl.handle.net/10042/to-12714</ref>
|- style="text-align: center;"
! Boat
| -231.602802<ref>[[File:Sbmod3BL2.LOG]]</ref>
| -231.450928<ref>[[File:Sbmod3BL2.LOG]]</ref>
|style="border-right: 2px solid grey;" | -231.445299 <ref>[[File:Sbmod3BL2.LOG]]</ref>
| -234.543093<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.402339<ref>http://hdl.handle.net/10042/to-12710</ref>
| -234.396005<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.378575<ref>http://hdl.handle.net/10042/to-12711</ref>
|}

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Transition energies relative to Anti2 (in kcal/mol)
|-
!
! colspan=2 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=3 style="border-right: 2px solid grey;" | DFT/6-31G*
! Expt.
|-
! State
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

600k
! 0k
|- style="text-align: center;"
! Chair
| 45.71
|style="border-right: 2px solid grey;" |44.70
| 34.07
| 33.18
| style="border-right: 2px solid grey;" | 32.72
| 33.5 ± 0.5
|- style="text-align: center;"
! Boat
| 55.60
|style="border-right: 2px solid grey;" |54.76
| 41.96
| 41.32
| style="border-right: 2px solid grey;" | 41.16
| 44.7 ± 2.0
|}

Both sets of calculations show that the chair transition structure is ~10kcal/mol lower in energy than the boat (as expected if compared to hexane structures) transition, however the second optimisation values are significantly closer to the experimental results. This demonstrates the greater accuracy of the DFT method over the HF optimisation. The DFT versions ~1kcal/mol out compared to the range of the experimental. This shows the calculations were done correctly, and demonstrates the accuracy of the DFT method.

==Diels-alder==

[[file:Sbmod3DAM.png|center]]
The diels-alder reaction is a cyclic addition of a alkene group to a cis conjugated diene as above. The alkene approaches and the reaction occurs due to strong orbital overlap viewable below.

To analyse this reaction, the transition state had to be predicted. This was done, as described above, by freezing the reacting bond distance at 2.2 angstroms, optimising, then optimising to a transition state with the reacting bonds set to derivative<ref>http://hdl.handle.net/10042/to-12719</ref>. The resulting transition structure shows a distinct negative synchronous vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3DAT.gif -957cm<sup>-1</sup>], confirming its nature as a transition state for the diels alder reaction. The transition state forming C-C bonds are 2.118<ref>http://hdl.handle.net/10042/to-12719</ref> angstroms long, which collapse to 1.519<ref>http://hdl.handle.net/10042/to-12720</ref> angstroms after a minimisation. In the
<jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DATS.mol</uploadedFileContents>
<text>'''transition state'''</text>
<script>background=black; measure 1 11; measure 14 8; measure 11 14; measure 1 4; measure 4 6; measure 6 8</script>
</jmolAppletLink>
</jmol>
the butadiene segment shows bond lengths (0.138-0.140nm) similar to benzene (0.14nm) This is due to the electron donation from the butadiene HOMO into the ethene LUMO, and the ethene HOMO into the butadiene LUMO. This results in a decrease in bond order between the alkene bonds (normally 0.134nm) and an increase in the bond order for the sp2 C-C butadiene bond due to the shape of the LUMO as below.

The table below shows the HOMO-LUMO orbitals of the molecules involves. They clearly show the HOMO of the transition state is the result of the ethene LUMO and the butadiene HOMO, which all share a symmetry, whilst the LUMO is formed from the thene HOMO and the butadiene LUMO, which share s symmetry.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+Orbitals
! molecule
! HOMO
(symmetry)
!LUMO
(symmetry)
|-
!rowspan=2|Butadiene<ref>http://hdl.handle.net/10042/to-12721</ref>
|[[file:Sbmod3BH.png|300px]]
|[[file:Sbmod3BL.png|300px]]
|-style="text-align: center;"
|a
|s
|-
!rowspan=2|Ethene<ref>http://hdl.handle.net/10042/to-12726</ref>
|[[file:Sbmod3EH.png|300px]]
|[[file:Sbmod3LH.png|300px]]
|-style="text-align: center;"
|s
|a
|-
!rowspan=2|Cyclohexene TS<ref>http://hdl.handle.net/10042/to-12719</ref>
|[[file:Sbmod3DATSH.png|300px]]
|[[file:Sbmod3DATSL.png|300px]]
|-style="text-align: center;"
|a
|s
|}

{| class="wikitable"; border="0"; style="margin: 1em auto 1em auto;"
|-style="text-align: center;"
|Endo
|width="200" |
|Exo
|-
|[[file:Sbmod3DAEnM.png|center]]
|
|[[file:Sbmod3DAExM.png|center]]
|-style="text-align: center;"
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3DAEnT.gif -810cm<sup>-1</sup>]
|
|[https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3DAExT.gif -814cm<sup>-1</sup>]
|}

After examining the basic Diels alder reaction, the above more complex version involving stereochemistry was subsequently analysed. In this reaction, the orientation of the attack determines the subsequent transition state and final molecule. This was done in an attempt to determine which product would be the kinetic and thermodynamic product. After starting with AM1 optimised starting reactants, the transition state for each orientation was found as above using the freeze and derivative method. After acquiring the AM1 transition states, they were further refined using the PM6 optimisation method. Using these transition states, an IRC was run to find the energy of the final products.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ energy comparison
|-
!
! colspan=3 style="border-right: 2px solid grey;" | AM1
! colspan=3 | PM6
|-
! Molecule
! Electronic energy
! New C-C length
! style="border-right: 2px solid grey;" | Through space
C-C length
! Electronic energy
! New C-C length
! Through space
C-C length
|-
! <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3Endots.mol</uploadedFileContents>
<text>Endo TS</text>
<script>background=black</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12727</ref><ref>http://hdl.handle.net/10042/to-12729</ref>
| -0.05121220
| 2.14913
|style="border-right: 2px solid grey;" | 2.85929
| -0.06243761
| 2.14913
| 2.85843
|-
! <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3Exots.mol</uploadedFileContents>
<text>Exo TS</text>
<script>background=black</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12728</ref><ref>http://hdl.handle.net/10042/to-12730</ref>
| -0.05027834
| 2.16151
|style="border-right: 2px solid grey;" | 2.93695
| -0.05981691
| 2.16377
| 2.93486
|-
! <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3Endo.mol</uploadedFileContents>
<text>Endo</text>
<script>background=black</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12727</ref><ref>http://hdl.handle.net/10042/to-12729</ref>
| -0.16017041
| 1.53587
|style="border-right: 2px solid grey;" | 2.98378
| -0.17125794
| 1.55749
| 2.92347
|-
! <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3Exo.mol</uploadedFileContents>
<text>Exo</text>
<script>background=black</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12728</ref><ref>http://hdl.handle.net/10042/to-12730</ref>

| -0.15990940
| 1.53608
|style="border-right: 2px solid grey;" | 2.94318
| -0.17163675
| 1.55678
| 2.95734
|}

The PM6 shows that the endo product is preferred kinetically due to the lower energy transition state, but the exo product has a lower final product and so is preferred thermodynamically. The noticable narrower endo transition state C C through space indicates secondary orbital overlap, viewable in LUMO2 + LUMO3 below, but absent in both the final product and both the exo transition state and final form. This stabilising interaction would explain the lower energy endo transition state and why it would be the preferred product.

{| class="wikitable"; border="0"; style="margin: 1em auto 1em auto;"
|-style="text-align: center;"
|LUMO+1
|width="200" |
|LUMO+2
|-
|[[file:Sbmod3DAEnL2.png|450px]]
|
|[[file:Sbmod3DAEnL3.png|400px]]
|}

<references/>

File:Sbmod3CIRC.gif

2012-02-20T16:23:01Z

Sb5009:

File:Sbmod3BIRC.gif

2012-02-20T16:23:01Z

Sb5009:

File:Sbmod3Endots.mol

2012-02-20T15:11:38Z

Sb5009:

File:Sbmod3Endo.mol

2012-02-20T15:11:38Z

Sb5009:

File:Sbmod3Exots.mol

2012-02-20T15:11:37Z

Sb5009:

File:Sbmod3Exo.mol

2012-02-20T15:11:37Z

Sb5009:

File:Sbmod3DAExnT.gif

2012-02-20T15:07:06Z

Sb5009:

File:Sbmod3DAEnT.gif

2012-02-20T15:07:05Z

Sb5009:

File:Sbmod3DAEnL3.png

2012-02-20T14:49:12Z

Sb5009:

File:Sbmod3DAEnL2.png

2012-02-20T14:49:11Z

Sb5009:

Rep:Mod:smb59mod3

2012-02-19T11:25:29Z

Sb5009:

==Cope rearrangement==

*picture of mechanism
*concerted pericyclic, bond forming transition is asymmetric

===1,5-hexadiene===

[[file:sbmod3HM.png|center]]
The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G, with both undergoing a frequency analysis to ensure the stationary point reached was a minimum.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 DFT B3LYP frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

===Transition states===
====Boat structure====
Following this, the chair and boat transition states were calculated using different methods. First, to form the chair transition state, two optimised (HF/3-21G) allyl fragments were placed (CH<sub>2</sub>CHCH<sub>2</sub>) approximating a hexane chair structure with the carbons with C<sub>2h</sub> symmetry. This was then optimised to a TS (berny), giving a single vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CV1.gif -818cm<sup>-1</sup>]<ref>[[file:Sbmod3CL1.LOG]]</ref>. Afterwards, a second method was used, via freezing the bond length between the reacting carbons to 2.2 angstroms, minimising using HF/3-21G, then minimising to a TS (berny) after setting the frozen bonds to derivative, giving a transitional vibration at -818cm<sup>-1</sup><ref>[[file:Sbmod3CL2B.LOG]]</ref> again, but with 2.0199 angstroms seperating the reacting carbons (Decreasing from 2.0206).
====Chair structure====
To form the C<sub>2v</sub> boat structure, the transition state was found using QST2, first using ther anti2 molecule above and renumbering the atoms to simulate the molecule before and after the transition. However, this failed initially due to the shape of anti2 <ref>[[file:Sbmod3CL1.LOG]]</ref>. This was improved upon by changing the inner dihedral angle to 0 and the inside carbon angles to 100', resulting in molecules similar to just before and after a transition. This resulted in a successful transition state formed, with a transition vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3BT.gif -840cm<sup>-1</sup>]<ref>[[file:Sbmod3CL2.LOG]]</ref>. An additional attempt to use the initial Anti2 molecules was successful by using QST3, which involves aiding the calculation by adding an approximated transition state. This lead to a near identical transition state at -840cm<sup>-1</sup><ref>http://hdl.handle.net/10042/to-12703</ref>

To demonstrate what occurs after the transition state, an IRC was performed (100 steps, force constants calculated each time, with final molecule optimised again, all using HF as above), demonstrating that the chair transition state ended forming the guache2<ref>http://hdl.handle.net/10042/to-12717 </ref><ref>http://hdl.handle.net/10042/to-12718</ref> product above after the transition step, while the boat initially formed gauche2, but subsequently minimised to form gauche3<ref>http://hdl.handle.net/10042/to-12715</ref><ref> http://hdl.handle.net/10042/to-12716</ref>

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti2 and transition state energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>http://hdl.handle.net/10042/to-12708</ref>
| -231.539540<ref>http://hdl.handle.net/10042/to-12708</ref>
| style="border-right: 2px solid grey;" | -231.532566<ref>http://hdl.handle.net/10042/to-12708</ref>
| -234.611710<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.469204<ref>http://hdl.handle.net/10042/to-12706</ref>
| -234.461857<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.444170<ref>http://hdl.handle.net/10042/to-12707</ref>
|- style="text-align: center;"
! Chair
| -231.619322<ref>File:Sbmod3CL2B.LOG</ref>
| -231.466696<ref>File:Sbmod3CL2B.LOG</ref>
|style="border-right: 2px solid grey;" | -231.461337<ref>File:Sbmod3CL2B.LOG</ref>
| -234.556981<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.414906<ref>http://hdl.handle.net/10042/to-12712</ref>
| -234.408982<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.392032<ref>http://hdl.handle.net/10042/to-12714</ref>
|- style="text-align: center;"
! Boat
| -231.602802<ref>File:Sbmod3BL2.LOG</ref>
| -231.450928<ref>File:Sbmod3BL2.LOG</ref>
|style="border-right: 2px solid grey;" | -231.445299 <ref>File:Sbmod3BL2.LOG</ref>
| -234.543093<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.402339<ref>http://hdl.handle.net/10042/to-12710</ref>
| -234.396005<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.378575<ref>http://hdl.handle.net/10042/to-12711</ref>
|}

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Transition energies relative to Anti2 (in kcal/mol)
|-
!
! colspan=2 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=3 style="border-right: 2px solid grey;" | DFT/6-31G*
! Expt.
|-
! State
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

600k
! 0k
|- style="text-align: center;"
! Chair
| 45.71
|style="border-right: 2px solid grey;" |44.70
| 34.07
| 33.18
| style="border-right: 2px solid grey;" | 32.72
| 33.5 ± 0.5
|- style="text-align: center;"
! Boat
| 55.60
|style="border-right: 2px solid grey;" |54.76
| 41.96
| 41.32
| style="border-right: 2px solid grey;" | 41.16
| 44.7 ± 2.0
|}

Both sets of calculations show that the chair transition structure is ~10kcal/mol lower in energy than the boat (as expected if compared to hexane structures) transition, however the second optimisation values are significantly closer to the experimental results. This demonstrates the greater accuracy of the DFT method over the HF optimisation. The DFT versions ~1kcal/mol out compared to the range of the experimental. This shows the calculations were done correctly, and demonstrates the accuracy of the DFT method.

==Diels alder==

*diels alder explanation
[[file:Sbmod3DAM.png|center]]

To analyse this reaction, the transition state had to be predicted. This was done, as described above, by freezing the reacting bond distance at 2.2 angstroms, optimising, then optimising to a transition state with the reacting bonds set to derivative<ref>http://hdl.handle.net/10042/to-12719</ref>. The resulting transition structure shows a distinct negative synchronous vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3DAT.gif -957cm<sup>-1</sup>], confirming its nature as a transition state for the diels alder reaction. The transition state forming C-C bonds are 2.118<ref>http://hdl.handle.net/10042/to-12719</ref> angstroms long, which collapse to 1.519<ref>http://hdl.handle.net/10042/to-12720</ref> angstroms after a minimisation. The butadiene segment shows bond lengths in between sp2 and sp3 lengths, due to the changing of bond orders in the
<jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DATS.mol</uploadedFileContents>
<text>'''transition state'''</text>
<script>background=black; measure 1 11; measure 14 8; measure 11 14; measure 1 4; measure 4 6; measure 6 8</script>
</jmolAppletLink>
</jmol>.
The table below shows the HOMO-LUMO orbitals of the molecules involves. They clearly show the HOMO of the transition state is the result of the ethene LUMO and the butadiene HOMO, which all share a symmetry, whilst the LUMO is formed from the thene HOMO and the butadiene LUMO, which share s symmetry.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+Orbitals
! molecule
! HOMO
(symmetry)
!LUMO
(symmetry)
|-
!rowspan=2|Butadiene<ref>http://hdl.handle.net/10042/to-12721</ref>
|[[file:Sbmod3BH.png|300px]]
|[[file:Sbmod3BL.png|300px]]
|-style="text-align: center;"
|a
|s
|-
!rowspan=2|Ethene
|[[file:Sbmod3EH.png|300px]]
|[[file:Sbmod3LH.png|300px]]
|-style="text-align: center;"
|s
|a
|-
!rowspan=2|Cyclohexene TS
|[[file:Sbmod3DATSH.png|300px]]
|[[file:Sbmod3DATSL.png|300px]]
|-style="text-align: center;"
|a
|s
|}

{| class="wikitable"; border="0"; style="margin: 1em auto 1em auto;"
|-style="text-align: center;"
|Endo
|width="200" |
|Exo
|-
|[[file:Sbmod3DAEnM.png|center]]
|
|[[file:Sbmod3DAExM.png|center]]
|}
part3

PM6 shows that endo is preferred kinetically, but exo is preferred thermodynamically, narrower endo through space indicates secondary orbital overlap, viewable in LUMO2 + LUMO3 .
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ energy comparison
|-
!
! colspan=3 style="border-right: 2px solid grey;" | AM1
! colspan=3 | PM6
|-
! Molecule
! Electronic energy
! New C-C length
! style="border-right: 2px solid grey;" | Through space
C-C length
! Electronic energy
! New C-C length
! Through space
C-C length
|-
! Endo TS
| -0.05121220
| 2.14913
|style="border-right: 2px solid grey;" | 2.85929
| -0.06243761
| 2.14913
| 2.85843
|-
! Exo TS
| -0.05027834
| 2.16151
|style="border-right: 2px solid grey;" | 2.93695
| -0.05981691
| 2.16377
| 2.93486
|-
! Endo
| -0.16017041
| 1.53587
|style="border-right: 2px solid grey;" | 2.98378
| -0.17125794
| 1.55749
| 2.92347
|-
! Exo
| -0.15990940
| 1.53608
|style="border-right: 2px solid grey;" | 2.94318
| -0.17163675
| 1.55678
| 2.95734
|}
|}

<references/>

File:Sbmod3LH.png

2012-02-19T10:53:47Z

Sb5009:

File:Sbmod3EH.png

2012-02-19T10:53:47Z

Sb5009:

File:Sbmod3DATS.mol

2012-02-19T10:36:59Z

Sb5009:

File:Sbmod3DATSL.png

2012-02-19T10:16:08Z

Sb5009:

File:Sbmod3DATSH.png

2012-02-19T10:16:07Z

Sb5009:

File:Sbmod3BL.png

2012-02-19T10:16:07Z

Sb5009:

File:Sbmod3BH.png

2012-02-19T10:16:07Z

Sb5009:

File:Sbmod3DAExM.png

2012-02-19T10:03:46Z

Sb5009:

File:Sbmod3DAEnM.png

2012-02-19T10:03:46Z

Sb5009:

File:Sbmod3DAM.png

2012-02-19T09:57:02Z

Sb5009:

File:Sbmod3HM.png

2012-02-19T09:55:27Z

Sb5009:

Rep:Mod:smb59mod3

2012-02-19T02:43:03Z

Sb5009:

==Cope rearrangement==

*picture of mechanism
*concerted pericyclic, bond forming transition is asymmetric

===1,5-hexadiene===
The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G, with both undergoing a frequency analysis to ensure the stationary point reached was a minimum.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 DFT B3LYP frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

===Transition states===
====Boat structure====
Following this, the chair and boat transition states were calculated using different methods. First, to form the chair transition state, two optimised (HF/3-21G) allyl fragments were placed (CH<sub>2</sub>CHCH<sub>2</sub>) approximating a hexane chair structure with the carbons with C<sub>2h</sub> symmetry. This was then optimised to a TS (berny), giving a single vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CV1.gif -818cm<sup>-1</sup>]<ref>[[file:Sbmod3CL1.LOG]]</ref>. Afterwards, a second method was used, via freezing the bond length between the reacting carbons to 2.2 angstroms, minimising using HF/3-21G, then minimising to a TS (berny) after setting the frozen bonds to derivative, giving a transitional vibration at -818cm<sup>-1</sup><ref>[[file:Sbmod3CL2B.LOG]]</ref> again, but with 2.0199 angstroms seperating the reacting carbons (Decreasing from 2.0206).
====Chair structure====
To form the C<sub>2v</sub> boat structure, the transition state was found using QST2, first using ther anti2 molecule above and renumbering the atoms to simulate the molecule before and after the transition. However, this failed initially due to the shape of anti2 <ref>[[file:Sbmod3CL1.LOG]]</ref>. This was improved upon by changing the inner dihedral angle to 0 and the inside carbon angles to 100', resulting in molecules similar to just before and after a transition. This resulted in a successful transition state formed, with a transition vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3BT.gif -840cm<sup>-1</sup>]<ref>[[file:Sbmod3CL2.LOG]]</ref>. An additional attempt to use the initial Anti2 molecules was successful by using QST3, which involves aiding the calculation by adding an approximated transition state. This lead to a near identical transition state at -840cm<sup>-1</sup><ref>http://hdl.handle.net/10042/to-12703</ref>

To demonstrate what occurs after the transition state, an IRC was performed (100 steps, force constants calculated each time, with final molecule optimised again, all using HF as above), demonstrating that the chair transition state ended forming the guache2<ref>http://hdl.handle.net/10042/to-12717 </ref><ref>http://hdl.handle.net/10042/to-12718</ref> product above after the transition step, while the boat initially formed gauche2, but subsequently minimised to form gauche3<ref>http://hdl.handle.net/10042/to-12715</ref><ref> http://hdl.handle.net/10042/to-12716</ref>

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti2 and transition state energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>http://hdl.handle.net/10042/to-12708</ref>
| -231.539540<ref>http://hdl.handle.net/10042/to-12708</ref>
| style="border-right: 2px solid grey;" | -231.532566<ref>http://hdl.handle.net/10042/to-12708</ref>
| -234.611710<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.469204<ref>http://hdl.handle.net/10042/to-12706</ref>
| -234.461857<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.444170<ref>http://hdl.handle.net/10042/to-12707</ref>
|- style="text-align: center;"
! Chair
| -231.619322<ref>File:Sbmod3CL2B.LOG</ref>
| -231.466696<ref>File:Sbmod3CL2B.LOG</ref>
|style="border-right: 2px solid grey;" | -231.461337<ref>File:Sbmod3CL2B.LOG</ref>
| -234.556981<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.414906<ref>http://hdl.handle.net/10042/to-12712</ref>
| -234.408982<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.392032<ref>http://hdl.handle.net/10042/to-12714</ref>
|- style="text-align: center;"
! Boat
| -231.602802<ref>File:Sbmod3BL2.LOG</ref>
| -231.450928<ref>File:Sbmod3BL2.LOG</ref>
|style="border-right: 2px solid grey;" | -231.445299 <ref>File:Sbmod3BL2.LOG</ref>
| -234.543093<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.402339<ref>http://hdl.handle.net/10042/to-12710</ref>
| -234.396005<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.378575<ref>http://hdl.handle.net/10042/to-12711</ref>
|}

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Transition energies relative to Anti2 (in kcal/mol)
|-
!
! colspan=2 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=3 style="border-right: 2px solid grey;" | DFT/6-31G*
! Expt.
|-
! State
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

600k
! 0k
|- style="text-align: center;"
! Chair
| 45.71
|style="border-right: 2px solid grey;" |44.70
| 34.07
| 33.18
| style="border-right: 2px solid grey;" | 32.72
| 33.5 ± 0.5
|- style="text-align: center;"
! Boat
| 55.60
|style="border-right: 2px solid grey;" |54.76
| 41.96
| 41.32
| style="border-right: 2px solid grey;" | 41.16
| 44.7 ± 2.0
|}

Both sets of calculations show that the chair transition structure is ~10kcal/mol lower in energy than the boat (as expected if compared to hexane structures) transition, however the second optimisation values are significantly closer to the experimental results. This demonstrates the greater accuracy of the DFT method over the HF optimisation. The DFT versions ~1kcal/mol out compared to the range of the experimental. This shows the calculations were done correctly, and demonstrates the accuracy of the DFT method.

==Diels alder==

*mechanism

*diels alder explanation

To analyse this reaction, the transition state had to be predicted. This was done, as described above, by freezing the reacting bond distance at 2.2 angstroms, optimising, then optimising to a transition state with the reacting bonds set to derivative<ref>http://hdl.handle.net/10042/to-12719</ref>. The resulting transition structure shows a distinct negative vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3DAT.gif -957cm<sup>-1</sup>], confirming its nature as a transition state.

TS C-C bond: 2.118 angstroms, symmetric bond formation suggests diels alder,
butadiene homo = a
butadiene lumo = s
DA homo = a
DA lumo = s

part3

PM6 shows that endo is preferred kinetically, but exo is preferred thermodynamically, narrower endo through space indicates secondary orbital overlap, viewable in LUMO2 + LUMO3 .
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ energy comparison
|-
!
! colspan=3 style="border-right: 2px solid grey;" | AM1
! colspan=3 | PM6
|-
! Molecule
! Electronic energy
! New C-C length
! style="border-right: 2px solid grey;" | Through space
C-C length
! Electronic energy
! New C-C length
! Through space
C-C length
|-
! Endo TS
| -0.05121220
| 2.14913
|style="border-right: 2px solid grey;" | 2.85929
| -0.06243761
| 2.14913
| 2.85843
|-
! Exo TS
| -0.05027834
| 2.16151
|style="border-right: 2px solid grey;" | 2.93695
| -0.05981691
| 2.16377
| 2.93486
|-
! Endo
| -0.16017041
| 1.53587
|style="border-right: 2px solid grey;" | 2.98378
| -0.17125794
| 1.55749
| 2.92347
|-
! Exo
| -0.15990940
| 1.53608
|style="border-right: 2px solid grey;" | 2.94318
| -0.17163675
| 1.55678
| 2.95734
|}
|}

<references/>

Rep:Mod:smb59mod3

2012-02-19T02:04:15Z

Sb5009:

==Cope rearrangement==

*picture of mechanism
*concerted pericyclic, bond forming transition is asymmetric

===1,5-hexadiene===
The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G, with both undergoing a frequency analysis to ensure the stationary point reached was a minimum.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 DFT B3LYP frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

===Transition states===
====Boat structure====
Following this, the chair and boat transition states were calculated using different methods. First, to form the chair transition state, two optimised (HF/3-21G) allyl fragments were placed (CH<sub>2</sub>CHCH<sub>2</sub>) approximating a hexane chair structure with the carbons with C<sub>2h</sub> symmetry. This was then optimised to a TS (berny), giving a single vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CV1.gif -818cm<sup>-1</sup>]<ref>[[file:Sbmod3CL1.LOG]]</ref>. Afterwards, a second method was used, via freezing the bond length between the reacting carbons to 2.2 angstroms, minimising using HF/3-21G, then minimising to a TS (berny) after setting the frozen bonds to derivative, giving a transitional vibration at -818cm<sup>-1</sup><ref>[[file:Sbmod3CL2B.LOG]]</ref> again, but with 2.0199 angstroms seperating the reacting carbons (Decreasing from 2.0206).
====Chair structure====
To form the C<sub>2v</sub> boat structure, the transition state was found using QST2, first using ther anti2 molecule above and renumbering the atoms to simulate the molecule before and after the transition. However, this failed initially due to the shape of anti2 <ref>[[file:Sbmod3CL1.LOG]]</ref>. This was improved upon by changing the inner dihedral angle to 0 and the inside carbon angles to 100', resulting in molecules similar to just before and after a transition. This resulted in a successful transition state formed, with a transition vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3BT.gif -840cm<sup>-1</sup>]<ref>[[file:Sbmod3CL2.LOG]]</ref>. An additional attempt to use the initial Anti2 molecules was successful by using QST3, which involves aiding the calculation by adding an approximated transition state. This lead to a near identical transition state at -840cm<sup>-1</sup><ref>http://hdl.handle.net/10042/to-12703</ref>

To demonstrate what occurs after the transition state, an IRC was performed (100 steps, force constants calculated each time, with final molecule optimised again, all using HF as above), demonstrating that the chair transition state ended forming the guache2<ref>http://hdl.handle.net/10042/to-12717 </ref><ref>http://hdl.handle.net/10042/to-12718</ref> product above after the transition step, while the boat initially formed gauche2, but subsequently minimised to form gauche3<ref>http://hdl.handle.net/10042/to-12715</ref><ref> http://hdl.handle.net/10042/to-12716</ref>

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti2 and transition state energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>http://hdl.handle.net/10042/to-12708</ref>
| -231.539540<ref>http://hdl.handle.net/10042/to-12708</ref>
| style="border-right: 2px solid grey;" | -231.532566<ref>http://hdl.handle.net/10042/to-12708</ref>
| -234.611710<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.469204<ref>http://hdl.handle.net/10042/to-12706</ref>
| -234.461857<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.444170<ref>http://hdl.handle.net/10042/to-12707</ref>
|- style="text-align: center;"
! Chair
| -231.619322<ref>File:Sbmod3CL2B.LOG</ref>
| -231.466696<ref>File:Sbmod3CL2B.LOG</ref>
|style="border-right: 2px solid grey;" | -231.461337<ref>File:Sbmod3CL2B.LOG</ref>
| -234.556981<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.414906<ref>http://hdl.handle.net/10042/to-12712</ref>
| -234.408982<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.392032<ref>http://hdl.handle.net/10042/to-12714</ref>
|- style="text-align: center;"
! Boat
| -231.602802<ref>File:Sbmod3BL2.LOG</ref>
| -231.450928<ref>File:Sbmod3BL2.LOG</ref>
|style="border-right: 2px solid grey;" | -231.445299 <ref>File:Sbmod3BL2.LOG</ref>
| -234.543093<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.402339<ref>http://hdl.handle.net/10042/to-12710</ref>
| -234.396005<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.378575<ref>http://hdl.handle.net/10042/to-12711</ref>
|}

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Transition energies relative to Anti2 (in kcal/mol)
|-
!
! colspan=2 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=3 style="border-right: 2px solid grey;" | DFT/6-31G*
! Expt.
|-
! State
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

600k
! 0k
|- style="text-align: center;"
! Chair
| 45.71
|style="border-right: 2px solid grey;" |44.70
| 34.07
| 33.18
| style="border-right: 2px solid grey;" | 32.72
| 33.5 ± 0.5
|- style="text-align: center;"
! Boat
| 55.60
|style="border-right: 2px solid grey;" |54.76
| 41.96
| 41.32
| style="border-right: 2px solid grey;" | 41.16
| 44.7 ± 2.0
|}

Both sets of calculations show that the chair transition structure is ~10kcal/mol lower in energy than the boat (as expected if compared to hexane structures) transition, however the second optimisation values are significantly closer to the experimental results. This demonstrates the greater accuracy of the DFT method over the HF optimisation. The DFT versions ~1kcal/mol out compared to the range of the experimental. This shows the calculations were done correctly, and demonstrates the accuracy of the DFT method.

==Diels alder==

*mechanism

*diels alder explanation

To analyse this reaction, the transition state had to be predicted. This was done, as described above, by freezing the reacting bond distance at 2.2 angstroms, optimising, then optimising to a transition state with the reacting bonds set to derivative<ref>http://hdl.handle.net/10042/to-12719</ref>. The resulting transition structure shows a distinct negative vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3DAT.gif -957cm<sup>-1</sup>], confirming its nature as a transition state.

TS C-C bond: 2.118 angstroms, symmetric bond formation suggests diels alder,
butadiene homo = a
butadiene lumo = s
DA homo = a
DA lumo = s

AM1:
endo TS E = -0.05121220
endo TS freq = -810
endo TS bond = 2.14913
endo bond "through space" =

endo E = -0.16017041
endo bond = 1.53587
endo bond "through space" = 2.98378
LUMO2 demonstrates clear secondary orbital overlap

exo TS E = -0.05027834
exo TS freq = -814
exo TS bond = 2.16151
exo bond "through space" =

exo E opt = -0.15990940
exo bond = 1.53608
exo bond "through space" = 2.94318

make .mol demonstrating c-c distances
ts secondary overlap

PM6:
endo TS E = -0.06243761
endo TS bond = 1.14913
endo bond "through space" = 2.85843

endo E = -0.17125794
endo bond = 1.55749
endo bond "through space" = 2.92347

exo TS E = -0.05981691
exo TS bond =2.16377
exo bond "through space" = 2.93486

exo E opt = -0.17163675
exo bond = 1.55678
exo bond "through space" = 2.95734

PM6 shows that endo is preferred kinetically, but exo is preferred thermodynamically!.

<references/>

Rep:Mod:smb59mod3

2012-02-19T01:16:46Z

Sb5009:

==Cope rearrangement==

*picture of mechanism
*concerted pericyclic, bond forming transition is asymmetric

===1,5-hexadiene===
The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G, with both undergoing a frequency analysis to ensure the stationary point reached was a minimum.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 DFT B3LYP frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

===Transition states===
====Boat structure====
Following this, the chair and boat transition states were calculated using different methods. First, to form the chair transition state, two optimised (HF/3-21G) allyl fragments were placed (CH<sub>2</sub>CHCH<sub>2</sub>) approximating a hexane chair structure with the carbons with C<sub>2h</sub> symmetry. This was then optimised to a TS (berny), giving a single vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CV1.gif -818cm<sup>-1</sup>]<ref>[[file:Sbmod3CL1.LOG]]</ref>. Afterwards, a second method was used, via freezing the bond length between the reacting carbons to 2.2 angstroms, minimising using HF/3-21G, then minimising to a TS (berny) after setting the frozen bonds to derivative, giving a transitional vibration at -818cm<sup>-1</sup><ref>[[file:Sbmod3CL2B.LOG]]</ref> again, but with 2.0199 angstroms seperating the reacting carbons (Decreasing from 2.0206).
====Chair structure====
To form the C<sub>2v</sub> boat structure, the transition state was found using QST2, first using ther anti2 molecule above and renumbering the atoms to simulate the molecule before and after the transition. However, this failed initially due to the shape of anti2 <ref>[[file:Sbmod3CL1.LOG]]</ref>. This was improved upon by changing the inner dihedral angle to 0 and the inside carbon angles to 100', resulting in molecules similar to just before and after a transition. This resulted in a successful transition state formed, with a transition vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3BT.gif -840cm<sup>-1</sup>]<ref>[[file:Sbmod3CL2.LOG]]</ref>. An additional attempt to use the initial Anti2 molecules was successful by using QST3, which involves aiding the calculation by adding an approximated transition state. This lead to a near identical transition state at -840cm<sup>-1</sup><ref>http://hdl.handle.net/10042/to-12703</ref>

To demonstrate what occurs after the transition state, an IRC was performed (100 steps, force constants calculated each time, with final molecule optimised again, all using HF as above), demonstrating that the chair transition state ended forming the guache2<ref>http://hdl.handle.net/10042/to-12717 </ref><ref>http://hdl.handle.net/10042/to-12718</ref> product above after the transition step, while the boat initially formed gauche2, but subsequently minimised to form gauche3<ref>http://hdl.handle.net/10042/to-12715</ref><ref> http://hdl.handle.net/10042/to-12716</ref>

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti2 and transition state energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>http://hdl.handle.net/10042/to-12708</ref>
| -231.539540<ref>http://hdl.handle.net/10042/to-12708</ref>
| style="border-right: 2px solid grey;" | -231.532566<ref>http://hdl.handle.net/10042/to-12708</ref>
| -234.611710<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.469204<ref>http://hdl.handle.net/10042/to-12706</ref>
| -234.461857<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.444170<ref>http://hdl.handle.net/10042/to-12707</ref>
|- style="text-align: center;"
! Chair
| -231.619322<ref>File:Sbmod3CL2B.LOG</ref>
| -231.466696<ref>File:Sbmod3CL2B.LOG</ref>
|style="border-right: 2px solid grey;" | -231.461337<ref>File:Sbmod3CL2B.LOG</ref>
| -234.556981<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.414906<ref>http://hdl.handle.net/10042/to-12712</ref>
| -234.408982<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.392032<ref>http://hdl.handle.net/10042/to-12714</ref>
|- style="text-align: center;"
! Boat
| -231.602802<ref>File:Sbmod3BL2.LOG</ref>
| -231.450928<ref>File:Sbmod3BL2.LOG</ref>
|style="border-right: 2px solid grey;" | -231.445299 <ref>File:Sbmod3BL2.LOG</ref>
| -234.543093<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.402339<ref>http://hdl.handle.net/10042/to-12710</ref>
| -234.396005<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.378575<ref>http://hdl.handle.net/10042/to-12711</ref>
|}

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Transition energies relative to Anti2 (in kcal/mol)
|-
!
! colspan=2 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=3 style="border-right: 2px solid grey;" | DFT/6-31G*
! Expt.
|-
! State
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

600k
! 0k
|- style="text-align: center;"
! Chair
| 45.71
|style="border-right: 2px solid grey;" |44.70
| 34.07
| 33.18
| style="border-right: 2px solid grey;" | 32.72
| 33.5 ± 0.5
|- style="text-align: center;"
! Boat
| 55.60
|style="border-right: 2px solid grey;" |54.76
| 41.96
| 41.32
| style="border-right: 2px solid grey;" | 41.16
| 44.7 ± 2.0
|}

Both sets of calculations show that the chair transition structure is ~10kcal/mol lower in energy than the boat (as expected if compared to hexane structures) transition, however the second optimisation values are significantly closer to the experimental results. This demonstrates the greater accuracy of the DFT method over the HF optimisation. The DFT versions ~1kcal/mol out compared to the range of the experimental. This shows the calculations were done correctly, and demonstrates the accuracy of the DFT method.

==Diels alder==

*mechanism

*diels alder explanation

To analyse this reaction, the transition state had to be predicted. This was done, as described above, by freezing the reacting bond distance at 2.2 angstroms, optimising, then optimising to a transition state with the reacting bonds set to derivative<ref>http://hdl.handle.net/10042/to-12719</ref>. The resulting transition structure shows a distinct negative vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3DAT.gif -957cm<sup>-1</sup>], confirming its nature as a transition state.

TS C-C bond: 2.118 angstroms, symmetric bond formation suggests diels alder,
butadiene homo = a
butadiene lumo = s
DA homo = a
DA lumo = s

endo TS E = -0.05121220
endo TS freq = -810
endo TS bond = 2.14913

endo E = -0.16017041
endo bond = 1.53587

exo TS E = -0.05027834
exo TS freq = -814
exo TS bond = 2.16151

exo E opt = -0.15990940
exo bond = 1.53608

<references/>

File:Sbmod3DAT.gif

2012-02-19T00:32:00Z

Sb5009:

File:Sbmod3BT.gif

2012-02-19T00:31:59Z

Sb5009:

Rep:Mod:smb59mod3

2012-02-18T23:59:12Z

Sb5009:

==Cope rearrangement==

*picture of mechanism

===1,5-hexadiene===
The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G, with both undergoing a frequency analysis to ensure the stationary point reached was a minimum.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 DFT B3LYP frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

===Transition states===
====Boat structure====
Following this, the chair and boat transition states were calculated using different methods. First, to form the chair transition state, two optimised (HF/3-21G) allyl fragments were placed (CH<sub>2</sub>CHCH<sub>2</sub>) approximating a hexane chair structure with the carbons with C<sub>2h</sub> symmetry. This was then optimised to a TS (berny), giving a single vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CV1.gif -818cm<sup>-1</sup>]<ref>[[file:Sbmod3CL1.LOG]]</ref>. Afterwards, a second method was used, via freezing the bond length between the reacting carbons to 2.2 angstroms, minimising using HF/3-21G, then minimising to a TS (berny) after setting the frozen bonds to derivative, giving a transitional vibration at -818cm<sup>-1</sup><ref>[[file:Sbmod3CL2B.LOG]]</ref> again, but with 2.0199 angstroms seperating the reacting carbons (Decreasing from 2.0206).
====Chair structure====
To form the C<sub>2v</sub> boat structure, the transition state was found using QST2, first using ther anti2 molecule above and renumbering the atoms to simulate the molecule before and after the transition. However, this failed initially due to the shape of anti2 <ref>[[file:Sbmod3CL1.LOG]]</ref>. This was improved upon by changing the inner dihedral angle to 0 and the inside carbon angles to 100', resulting in molecules similar to just before and after a transition. This resulted in a successful transition state formed, with a transition vibration at -840cm<sup>-1</sup><ref>[[file:Sbmod3CL2.LOG]]</ref>. An additional attempt to use the initial Anti2 molecules was successful by using QST3, which involves aiding the calculation by adding an approximated transition state. This lead to a near identical transition state at -840cm<sup>-1</sup><ref>http://hdl.handle.net/10042/to-12703</ref>

To demonstrate what occurs after the transition state, an IRC was performed (100 steps, force constants calculated each time, with final molecule optimised again, all using HF as above), demonstrating that the chair transition state ended forming the guache2<ref>http://hdl.handle.net/10042/to-12717 </ref><ref>http://hdl.handle.net/10042/to-12718</ref> product above after the transition step, while the boat initially formed gauche2, but subsequently minimised to form gauche3<ref>http://hdl.handle.net/10042/to-12715</ref><ref> http://hdl.handle.net/10042/to-12716</ref>

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti2 and transition state energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>http://hdl.handle.net/10042/to-12708</ref>
| -231.539540<ref>http://hdl.handle.net/10042/to-12708</ref>
| style="border-right: 2px solid grey;" | -231.532566<ref>http://hdl.handle.net/10042/to-12708</ref>
| -234.611710<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.469204<ref>http://hdl.handle.net/10042/to-12706</ref>
| -234.461857<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.444170<ref>http://hdl.handle.net/10042/to-12707</ref>
|- style="text-align: center;"
! Chair
| -231.619322<ref>File:Sbmod3CL2B.LOG</ref>
| -231.466696<ref>File:Sbmod3CL2B.LOG</ref>
|style="border-right: 2px solid grey;" | -231.461337<ref>File:Sbmod3CL2B.LOG</ref>
| -234.556981<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.414906<ref>http://hdl.handle.net/10042/to-12712</ref>
| -234.408982<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.392032<ref>http://hdl.handle.net/10042/to-12714</ref>
|- style="text-align: center;"
! Boat
| -231.602802<ref>File:Sbmod3BL2.LOG</ref>
| -231.450928<ref>File:Sbmod3BL2.LOG</ref>
|style="border-right: 2px solid grey;" | -231.445299 <ref>File:Sbmod3BL2.LOG</ref>
| -234.543093<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.402339<ref>http://hdl.handle.net/10042/to-12710</ref>
| -234.396005<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.378575<ref>http://hdl.handle.net/10042/to-12711</ref>
|}

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Transition energies relative to Anti2 (in kcal/mol)
|-
!
! colspan=2 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=3 style="border-right: 2px solid grey;" | DFT/6-31G*
! Expt.
|-
! State
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

600k
! 0k
|- style="text-align: center;"
! Chair
| 45.71
|style="border-right: 2px solid grey;" |44.70
| 34.07
| 33.18
| style="border-right: 2px solid grey;" | 32.72
| 33.5 ± 0.5
|- style="text-align: center;"
! Boat
| 55.60
|style="border-right: 2px solid grey;" |54.76
| 41.96
| 41.32
| style="border-right: 2px solid grey;" | 41.16
| 44.7 ± 2.0
|}

Both sets of calculations show that the chair transition structure is ~10kcal/mol lower in energy than the boat (as expected if compared to hexane structures) transition, however the second optimisation values are significantly closer to the experimental results. This demonstrates the greater accuracy of the DFT method over the HF optimisation. The DFT versions ~1kcal/mol out compared to the range of the experimental. This shows the calculations were done correctly, and demonstrates the accuracy of the DFT method.

==Diels alder==
<references/>

Rep:Mod:smb59mod3

2012-02-18T23:26:24Z

Sb5009:

==Cope rearrangement==

*picture of mechanism

===1,5-hexadiene===
The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G, with both undergoing a frequency analysis to ensure the stationary point reached was a minimum.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 DFT B3LYP frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

===Transition states===
====Boat structure====
Following this, the chair and boat transition states were calculated using different methods. First, to form the chair transition state, two optimised (HF/3-21G) allyl fragments were placed (CH<sub>2</sub>CHCH<sub>2</sub>) approximating a hexane chair structure with the carbons with C<sub>2h</sub> symmetry. This was then optimised to a TS (berny), giving a single vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CV1.gif -818cm<sup>-1</sup>]<ref>[[file:Sbmod3CL1.LOG]]</ref>. Afterwards, a second method was used, via freezing the bond length between the reacting carbons to 2.2 angstroms, minimising using HF/3-21G, then minimising to a TS (berny) after setting the frozen bonds to derivative, giving a transitional vibration at -818cm<sup>-1</sup><ref>[[file:Sbmod3CL2B.LOG]]</ref> again, but with 2.0199 angstroms seperating the reacting carbons (Decreasing from 2.0206).
====Chair structure====
To form the C<sub>2v</sub> boat structure, the transition state was found using QST2, first using ther anti2 molecule above and renumbering the atoms to simulate the molecule before and after the transition. However, this failed initially due to the shape of anti2 <ref>[[file:Sbmod3CL1.LOG]]</ref>. This was improved upon by changing the inner dihedral angle to 0 and the inside carbon angles to 100', resulting in molecules similar to just before and after a transition. This resulted in a successful transition state formed, with a transition vibration at -840cm<sup>-1</sup><ref>[[file:Sbmod3CL2.LOG]]</ref>. An additional attempt to use the initial Anti2 molecules was successful by using QST3, which involves aiding the calculation by adding an approximated transition state. This lead to a near identical transition state at -840cm<sup>-1</sup><ref>http://hdl.handle.net/10042/to-12703</ref>

To demonstrate what occurs after the transition state, an IRC was performed, demonstrating that the chair transition state ended forming the guache2 product above after the transition step, while the boat

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti2 and transition state energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>http://hdl.handle.net/10042/to-12708</ref>
| -231.539540<ref>http://hdl.handle.net/10042/to-12708</ref>
| style="border-right: 2px solid grey;" | -231.532566<ref>http://hdl.handle.net/10042/to-12708</ref>
| -234.611710<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.469204<ref>http://hdl.handle.net/10042/to-12706</ref>
| -234.461857<ref>http://hdl.handle.net/10042/to-12704</ref>
| -234.444170<ref>http://hdl.handle.net/10042/to-12707</ref>
|- style="text-align: center;"
! Chair
| -231.619322<ref>File:Sbmod3CL2B.LOG</ref>
| -231.466696<ref>File:Sbmod3CL2B.LOG</ref>
|style="border-right: 2px solid grey;" | -231.461337<ref>File:Sbmod3CL2B.LOG</ref>
| -234.556981<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.414906<ref>http://hdl.handle.net/10042/to-12712</ref>
| -234.408982<ref>http://hdl.handle.net/10042/to-12713</ref>
| -234.392032<ref>http://hdl.handle.net/10042/to-12714</ref>
|- style="text-align: center;"
! Boat
| -231.602802<ref>File:Sbmod3BL2.LOG</ref>
| -231.450928<ref>File:Sbmod3BL2.LOG</ref>
|style="border-right: 2px solid grey;" | -231.445299 <ref>File:Sbmod3BL2.LOG</ref>
| -234.543093<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.402339<ref>http://hdl.handle.net/10042/to-12710</ref>
| -234.396005<ref>http://hdl.handle.net/10042/to-12709</ref>
| -234.378575<ref>http://hdl.handle.net/10042/to-12711</ref>
|}

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Transition energies relative to Anti2 (in kcal/mol)
|-
!
! colspan=2 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=3 style="border-right: 2px solid grey;" | DFT/6-31G*
! Expt.
|-
! State
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

600k
! 0k
|- style="text-align: center;"
! Chair
| 45.71
|style="border-right: 2px solid grey;" |44.70
| 34.07
| 33.18
| style="border-right: 2px solid grey;" | 32.72
| 33.5 ± 0.5
|- style="text-align: center;"
! Boat
| 55.60
|style="border-right: 2px solid grey;" |54.76
| 41.96
| 41.32
| style="border-right: 2px solid grey;" | 41.16
| 44.7 ± 2.0
|}

This demonstrates the greater accuracy of the DFT method over the HF optimisation. The calculated values are very close to the experimental ones, with the DFT versiosn ~1kcal/mol out compared to the range of the experimental. This shows the calculations were done correctly, and demonstrates the accuracy of the DFT method.

Unable to finish section today due to SCAN refusing to be accessed.

==Diels alder==
<references/>

Rep:Mod:smb59mod3

2012-02-18T17:05:10Z

Sb5009:

==Cope rearrangement==

*picture of mechanism

The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G, with both undergoing a frequency analysis to ensure the stationary point reached was a minimum.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 DFT B3LYP frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

Following this, the chair and boat transition states were calculated using different methods. First, to form the chair transition state, two optimised (HF/3-21G) allyl fragments were placed (CH<sub>2</sub>CHCH<sub>2</sub>) approximating a hexane chair structure with the carbons with C<sub>2h</sub> symmetry. This was then optimised to a TS (berny), giving a single vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CV1.gif -818cm<sup>-1</sup>]<ref>[[file:Sbmod3CL1.LOG]]</ref>. Afterwards, a second method was used, via freezing the bond length between the reacting carbons to 2.2 angstroms, minimising using HF/3-21G, then minimising to a TS (berny) after setting the frozen bonds to derivative, giving a transitional vibration at -818cm<sup>-1</sup><ref>[[file:Sbmod3CL2B.LOG]]</ref> again, but with 2.0199 angstroms seperating the reacting carbons (Decreasing from 2.0206).

To form the C<sub>2v</sub> boat structure, the transition state was found using QST2, first using ther anti2 molecule above and renumbering the atoms to simulate the molecule before and after the transition. However, this failed initially due to the shape of anti2 <ref>[[file:Sbmod3CL1.LOG]]</ref>. This was improved upon by changing the inner dihedral angle to 0 and the inside carbon angles to 100', resulting in molecules similar to just before and after a transition. This resulted in a successful transition state formed, with a transition vibration at -840cm<sup>-1</sup><ref>[[file:Sbmod3CL2.LOG]]</ref>. An additional attempt to use the initial Anti2 molecules was successful by using QST3, which involves aiding the calculation by adding an approximated transition state. this lead to a near identical transition state at 840 By creating the approximate the molecule before and after the transition state, and QST3 by the addition of an approximated transition state at -840cm<sup>-1</sup><ref></ref>

To demonstrate what occurs after the transition state, an IRC was performed, demonstrating that the chair transition state ended forming the guache2 product above after the transition step, while the boat

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti2 and transition state energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>[[File:Sbmod3A2.LOG]]</ref>
| -231.539540
| style="border-right: 2px solid grey;" | -231.532566
| -234.611710
| -234.469204
| -234.461857
| -234.444170
|- style="text-align: center;"
! Chair
| -231.619322
| -231.466696
|style="border-right: 2px solid grey;" | -231.461337
| -234.556981
| -234.414906
| -234.408982
| -234.392032
|- style="text-align: center;"
! Boat
| -231.602802
| -231.450928
|style="border-right: 2px solid grey;" | -231.445299
| -234.543093
| -234.402339
| -234.396005
| -234.378575
|}

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Transition energies relative to Anti2 (in kcal/mol)
|-
!
! colspan=2 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=3 style="border-right: 2px solid grey;" | DFT/6-31G*
! Expt.
|-
! State
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

600k
! 0k
|- style="text-align: center;"
! Chair
| 45.71
|style="border-right: 2px solid grey;" |44.70
| 34.07
| 33.18
| style="border-right: 2px solid grey;" | 32.72
| 33.5 ± 0.5
|- style="text-align: center;"
! Boat
| 55.60
|style="border-right: 2px solid grey;" |54.76
| 41.96
| 41.32
| style="border-right: 2px solid grey;" | 41.16
| 44.7 ± 2.0
|}

This demonstrates the greater accuracy of the DFT method over the HF optimisation. The calculated values are very close to the experimental ones, with the DFT versiosn ~1kcal/mol out compared to the range of the experimental. This shows the calculations were done correctly, and demonstrates the accuracy of the DFT method.

Unable to finish section today due to SCAN refusing to be accessed.

==Diels alder==
<references/>

Rep:Mod:smb59mod3

2012-02-18T17:03:07Z

Sb5009:

Rep:Mod:smb59mod3

2012-02-18T16:56:02Z

Sb5009:

==Cope rearrangement==

*picture of mechanism

The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G, with both undergoing a frequency analysis to ensure the stationary point reached was a minimum.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 DFT B3LYP frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

Following this, the chair and boat transition states were calculated using different methods. First, to form the chair transition state, two optimised (HF/3-21G) allyl fragments were placed (CH<sub>2</sub>CHCH<sub>2</sub>) approximating a hexane chair structure with the carbons with C<sub>2h</sub> symmetry. This was then optimised to a TS (berny), giving a single vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CV1.gif -818cm<sup>-1</sup>]<ref>[[file:Sbmod3CL1.LOG]]</ref>. Afterwards, a second method was used, via freezing the bond length between the reacting carbons to 2.2 angstroms, minimising using HF/3-21G, then minimising to a TS (berny) after setting the frozen bonds to derivative, giving a transitional vibration at -818cm<sup>-1</sup><ref>[[file:Sbmod3CL2B.LOG]]</ref> again, but with 2.0199 angstroms seperating the reacting carbons (Decreasing from 2.0206).

To form the C<sub>2v</sub> boat structure, the transition state was found using QST2, first using ther anti2 molecule above and renumbering the atoms to simulate the molecule before and after the transition. However, this failed initially due to the shape of anti2 <ref>[[file:Sbmod3CL1.LOG]]</ref>. This was improved upon by changing the inner dihedral angle to 0 and the inside carbon angles to 100', resulting in molecules similar to just before and after a transition. This resulted in a successful transition state formed, with a transition vibration at -840cm<sup>-1</sup><ref>[[file:Sbmod3CL2.LOG]]</ref>. An additional attempt to use the initial Anti2 molecules was successful by using QST3, which involves aiding the calculation by adding an approximated transition state. this lead to a near identical transition state at 840 By creating the approximate the molecule before and after the transition state, and QST3 by the addition of an approximated transition state at -840cm<sup>-1</sup><ref></ref>

To demonstrate what occurs after the transition state, an IRC was performed, demonstrating that the chair transition state ended forming the guache2 product above after the transition step, while the boat

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti2 and transition state energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>[[File:Sbmod3A2.LOG]]</ref>
| -231.539540
| style="border-right: 2px solid grey;" | -231.532566
| -234.611710
| -234.469204
| -234.461857
| -234.444170
|- style="text-align: center;"
! Chair
| -231.619322
| -231.466696
|style="border-right: 2px solid grey;" | -231.461337
| -234.556981
| -234.414906
| -234.408982
| -234.392032
|- style="text-align: center;"
! Boat
| -231.602802
| -231.450928
|style="border-right: 2px solid grey;" | -231.445299
| -234.543093
| -234.402339
| -234.396005
| -234.378575
|}

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Transition energies relative to Anti2 (in kcal/mol)
|-
!
! colspan=2 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=3 style="border-right: 2px solid grey;" | DFT/6-31G*
! Expt.
|-
! State
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

600k
! 0k
|- style="text-align: center;"
! Chair
| 45.71
|style="border-right: 2px solid grey;" |44.70
| 34.07
| 33.18
| style="border-right: 2px solid grey;" | 32.72
| 33.5 ± 0.5
|- style="text-align: center;"
! Boat
| 55.60
|style="border-right: 2px solid grey;" |54.76
| 41.96
| 41.32
| style="border-right: 2px solid grey;" | 41.16
| 44.7 ± 2.0
|}

Unable to finish section today due to SCAN refusing to be accessed.

<references/>

Rep:Mod:smb59mod3

2012-02-18T16:42:20Z

Sb5009:

==Cope rearrangement==

*picture of mechanism

The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G, with both undergoing a frequency analysis to ensure the stationary point reached was a minimum.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 DFT B3LYP frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

Following this, the chair and boat transition states were calculated using different methods. First, to form the chair transition state, two optimised (HF/3-21G) allyl fragments were placed (CH<sub>2</sub>CHCH<sub>2</sub>) approximating a hexane chair structure with the carbons with C<sub>2h</sub> symmetry. This was then optimised to a TS (berny), giving a single vibration at [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:Sbmod3CV1.gif -818cm<sup>-1</sup>]<ref>[[file:Sbmod3CL1.LOG]]</ref>. Afterwards, a second method was used, via freezing the bond length between the reacting carbons to 2.2 angstroms, minimising using HF/3-21G, then minimising to a TS (berny) after setting the frozen bonds to derivative, giving a transitional vibration at -818cm<sup>-1</sup><ref>[[file:Sbmod3CL2B.LOG]]</ref> again, but with 2.0199 angstroms seperating the reacting carbons (Decreasing from 2.0206).

To form the C<sub>2v</sub> boat structure, the transition state was found using QST2, first using ther anti2 molecule above and renumbering the atoms to simulate the molecule before and after the transition. However, this failed initially due to the shape of anti2 <ref>[[file:Sbmod3CL1.LOG]]</ref>. This was improved upon by changing the inner dihedral angle to 0 and the inside carbon angles to 100', resulting in molecules similar to just before and after a transition. This resulted in a successful transition state formed, with a transition vibration at -840cm<sup>-1</sup><ref>[[file:Sbmod3CL2.LOG]]</ref>. An additional attempt to use the initial Anti2 molecules was successful by using QST3, which involves aiding the calculation by adding an approximated transition state. this lead to a near identical transition state at 840 By creating the approximate the molecule before and after the transition state, and QST3 by the addition of an approximated transition state at -840cm<sup>-1</sup><ref></ref>

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti2 and transition state energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>[[File:Sbmod3A2.LOG]]</ref>
| -231.539540
| style="border-right: 2px solid grey;" | -231.532566
| -234.611710
| -234.469204
| -234.461857
| -234.444170
|- style="text-align: center;"
! Chair
| -231.619322
| -231.466696
|style="border-right: 2px solid grey;" | -231.461337
| -234.556981
| -234.414906
| -234.408982
| -234.392032
|- style="text-align: center;"
! Boat
| -231.602802
| -231.450928
|style="border-right: 2px solid grey;" | -231.445299
| -234.543093
| -234.402339
| -234.396005
| -234.378575
|}

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Transition energies relative to Anti2 (in kcal/mol)
|-
!
! colspan=2 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=3 style="border-right: 2px solid grey;" | DFT/6-31G*
! Expt.
|-
! State
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

600k
! 0k
|- style="text-align: center;"
! Chair
| 45.71
|style="border-right: 2px solid grey;" |44.70
| 34.07
| 33.18
| style="border-right: 2px solid grey;" | 32.72
| 33.5 ± 0.5
|- style="text-align: center;"
! Boat
| 55.60
|style="border-right: 2px solid grey;" |54.76
| 41.96
| 41.32
| style="border-right: 2px solid grey;" | 41.16
| 44.7 ± 2.0
|}

Unable to finish section today due to SCAN refusing to be accessed.

<references/>

File:Sbmod3BL2.LOG

2012-02-18T16:39:56Z

Sb5009:

File:Sbmod3BL1.LOG

2012-02-18T16:39:55Z

Sb5009:

File:Sbmod3CV1.gif

2012-02-18T16:08:50Z

Sb5009:

File:Sbmod3CL2B.LOG

2012-02-18T16:08:49Z

Sb5009:

File:Sbmod3CL2.LOG

2012-02-18T16:08:48Z

Sb5009:

File:Sbmod3CL1.LOG

2012-02-18T16:08:48Z

Sb5009:

Rep:Mod:smb59mod3

2012-02-17T16:59:46Z

Sb5009:

==Cope rearrangement==

*picture of mechanism

The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>[[File:Sbmod3A2.LOG]]</ref>
| -231.539540
|style="border-right: 2px solid grey;" | -231.532566
| -234.611710
| -234.469204
| -234.461857
| -234.444170
|- style="text-align: center;"
! Chair
| -
| -
|style="border-right: 2px solid grey;" |
| -
| -
| -
| -
|- style="text-align: center;"
! Boat
|
|-231.450928
|style="border-right: 2px solid grey;" | -231.445299
|
|
|
|
|}

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

*add enthalpies
*compare the chair and boat bits
*compare with lit

<references/>

Rep:Mod:smb59mod3

2012-02-17T16:59:22Z

Sb5009:

==Cope rearrangement==

*picture of mechanism

The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|- style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|- style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 energies (in hartrees)
|-
!
! colspan=3 style="border-right: 2px solid grey;" | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
!style="border-right: 2px solid grey;" | Sum of electronic
and thermal Energies

298.15k
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies

298.15k
! Sum of electronic
and thermal Energies

600k
|- style="text-align: center;"
! 1,5-Hexadiene
| -231.69254<ref>[[File:Sbmod3A2.LOG]]</ref>
| -231.539540
|style="border-right: 2px solid grey;" | -231.532566
| -234.611710
| -234.469204
| -234.461857
| -234.444170
|- style="text-align: center;"
! Chair
| -
| -
|style="border-right: 2px solid grey;" |
| -
| -
| -
| -
|- style="text-align: center;"
! Boat
|
|-231.450928
|style="border-right: 2px solid grey;" | -231.445299
|
|
|
|
|}

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

*compare the chair and boat bits
*compare with lit

<references/>

Rep:Mod:smb59mod3

2012-02-17T14:56:10Z

Sb5009:

==Cope rearrangement==

*picture of mechanism

The cope rearrangement as shown involves a [3,3]-sigmatropic shift mechanism as above. To study this, first the various low energy conformers of 1,5-hexadiene were identified, then using the possible transition structures (boat and chair) are analyzed and compared.

After forming a rough outline of the conformers, they were minimised by HF/3-21G first to get a good approximation, then the approximation was refined using the more accurate DFT B3LYP/3-21G.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ 1,5-hexadiene
! Conformer
! Symmetry
! HF/3-21G
Hartrees
! HF/3-21G
relative kcal/mol
! DFT B3LYP/3-21G
Hartrees
! DFT B3LYP/3-21G
relative kcal/mol
|-style="text-align: center;"
! Gauche1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG1.mol</uploadedFileContents>
<text>-231.68772</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12539</ref>
| 3.10
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG1.mol</uploadedFileContents>
<text>-233.33245</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12528</ref>
| 2.48
|-style="text-align: center;"
! Gauche2
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG2.mol</uploadedFileContents>
<text>-231.69167</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12540</ref>
| 0.62
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG2.mol</uploadedFileContents>
<text>-233.33524</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12529</ref>
|0.73
|-style="text-align: center;"
! Gauche3
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG3.mol</uploadedFileContents>
<text>-231.69266</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G3.LOG]]</ref>
| 0.00
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG3.mol</uploadedFileContents>
<text>-233.33636</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12530</ref>
| 0.03
|-style="text-align: center;"
! Gauche4
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG4.mol</uploadedFileContents>
<text>-231.69153</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3G4.LOG]]</ref>
| 0.71
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG4.mol</uploadedFileContents>
<text>-233.33540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12531</ref>
| 0.63
|-style="text-align: center;"
! Gauche5
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG5.mol</uploadedFileContents>
<text>-231.68962</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12541</ref>
| 1.91
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG5.mol</uploadedFileContents>
<text>-233.33385</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12532</ref>
| 1.61
|-style="text-align: center;"
! Gauche6
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFG6.mol</uploadedFileContents>
<text>-231.68916</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12542</ref>
| 2.20
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTG6.mol</uploadedFileContents>
<text>-233.33345</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12533</ref>
| 1.86
|-style="text-align: center;"
! Anti1
| C<sub>2</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA1.mol</uploadedFileContents>
<text>-231.69260</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A1.LOG]]</ref>
| 0.04
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA1.mol</uploadedFileContents>
<text>-233.33641</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12534</ref>
| 0.00
|-style="text-align: center;"
! Anti2
| C<sub>i</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA2.mol</uploadedFileContents>
<text>-231.69254</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[File:Sbmod3A2.LOG]]</ref>
| 0.08
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA2.mol</uploadedFileContents>
<text>-233.33634</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12535</ref>
| 0.04
|-style="text-align: center;"
! Anti3
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA3.mol</uploadedFileContents>
<text>-231.68907</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12543</ref>
| 2.25
| <jmol>
<jmolAppletLink>
<uploadedFileContents>ASbmod3DFTA3.mol</uploadedFileContents>
<text>-233.33380</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12536</ref>
| 1.64
|-style="text-align: center;"
! Anti4
| C<sub>1</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA4.mol</uploadedFileContents>
<text>-231.69097</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12544</ref>
| 1.06
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA4.mol</uploadedFileContents>
<text>-233.33521</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12537</ref>
| 0.75
|-style="text-align: center;"
! Anti5
| C<sub>2h</sub>
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3HFA5.mol</uploadedFileContents>
<text>-231.68540</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>[[file:Sbmod3A5.LOG]]</ref>
| 4.56
| <jmol>
<jmolAppletLink>
<uploadedFileContents>Sbmod3DFTA5.mol</uploadedFileContents>
<text>-233.32932</text>
<script>background=black; measure 1 4 6 9; measure 4 6 9 12; measure 6 9 12 14</script>
</jmolAppletLink>
</jmol><ref>http://hdl.handle.net/10042/to-12545</ref>
| 4.45
|}

Using the butane analogy, where antiperiplanar is the lowest energy dihedral angle, Anti4 was formed, but due to the alkene parts of the molecule, a dihedral angle of 120' was preferred when involving them (while maintaining antiperiplanar for the central four carbons), resulting in Anti4 being the highest energy conformer.

This demonstrates that the HF optimization is a very close approximation, as the relative energies and the dihedral bond angles are all very similar to the more accurate DFT optimization, with only minor fraction of an angle changes through the different conformers, maintaining the same symmetry in all cases

As expected, the more accurate DFT B3LYP/3-21G game energies with lower values (~1.5 Hartrees), but the relative energies remained very similar. In all bar gauche2 and gauche3, the second optimisation resulted in reducing the energy difference between the comformers. Additionally, whilst the lowest energy conformer initially was gauche2, after the second optimisation the lowest was anti1, however the energy difference is so small (less than 0.1kcal/mol), that these two and anti2 can be considered essentially equally the lowest energy conformers.

Following this, the anti2 conformer was chosen for additional analysis, undergoing DFT B3LYP/6-31G* optimisation and a frequency analysis at 298.15 and 0.0001 kelvin using Freq=ReadIsotopes.

{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 energies
|-
!
! colspan=5 | HF/3-21G
! colspan=5 | DFT/6-31G*
|-
! State
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies
! Sum of electronic
and thermal Enthalpies
! Sum of electronic
and thermal Free Energies
! Electronic energy
! Sum of electronic
and zero-point Energies
! Sum of electronic
and thermal Energies
! Sum of electronic
and thermal Enthalpies
! Sum of electronic
and thermal Free Energies
|}

[[file:sbmod3A2F.png|center]]
{| class="wikitable" style="text-align: center;" style="margin: 1em auto 1em auto;"
|+ Anti 2 frequencies
! Stretch
! Frequency
! Magnitude
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F1.gif View]
| 670
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F2.gif View]
| 940
| 61
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F3.gif View]
| 1035
| 20
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F4.gif View]
| 1734
| 18
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F5.gif View]
| 3031
| 54
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F6.gif View]
| 3080
| 36
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F7.gif View]
| 3137
| 56
|-style="text-align: center;"
| [https://wiki.ch.ic.ac.uk/wiki/index.php?title=file:sbmod3A2F8.gif View]
| 3234
| 45
|-
|}

*compare the chair and boat bits
*compare with lit

<references/>

File:Sbmod3A2F8.gif

2012-02-17T13:35:02Z

Sb5009:

File:Sbmod3A2F7.gif

2012-02-17T13:35:01Z

Sb5009:

File:Sbmod3A2F6.gif

2012-02-17T13:35:01Z

Sb5009:

File:Sbmod3A2F5.gif

2012-02-17T13:35:00Z

Sb5009:

File:Sbmod3A2F4.gif

2012-02-17T13:35:00Z

Sb5009: