ChemWiki - User contributions [en]

Rep:Mod:maw210

2012-12-07T16:50:09Z

Maw210: /* The Diels-Alder Reaction */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

Note: Solvent effects are ignored.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. This is consistent with the obtained calculations: The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, but the endo TS has a slightly lower energy than the exo TS, hence the endo structure is kinetically favoured.

The HOMO of the endo and exo transition states are shown below. As expected, the endo HOMO is lower in energy than the exo HOMO. Both HOMOs are antisymmetric with respect to the plane. It is interesting to see that there is an absence of MO lobes around the -(C=O)-O-(C=O)- fragment. This is not the expected outcome of the secondary orbital overlap effect, since the SOO predicts that bonding interactions exist between the -(C=O)-O-(C=O)- fragment and the newly forming double bond. This suggests that either (a) the computational methods used to visualise these orbitals are not accurate enough, or that (b) the secondary orbital overlap is a useful way of rationalising the favoured formation of the endo product, but its validity is questionable.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

The table below summarises key C-C bond lengths in the endo and exo transition states. This includes directly bonded carbons and through space interactions of carbons.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

The partly formed σ C-C bonds have nearly the same distance in both endo and exo structures. In both structures the C3-C4 and C5-C6 bond lenghts are slightly longer than that of a typical C=C double bond (1.33 Å), indicating that the C3-C4 and C5-C6 bonds are reacting to form single bonded carbons. The C4-C5 bond is shorter than that of a typical C-C single bond (1.52 Å), which indicates that a double bond is forming.

The C1-C4/ C8-C5 through space distance in the endo product is shorter than the C1-C9/ C8-C10 interaction in the exo product. The shorter distance (i.e. larger strain) in the endo product is a trade off for the favourable secondary orbital overlap interactions observed in the transition state.

= References =

<references/>

Rep:Mod:maw210

2012-12-07T16:49:19Z

Maw210: /* Exo Product */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. This is consistent with the obtained calculations: The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, but the endo TS has a slightly lower energy than the exo TS, hence the endo structure is kinetically favoured.

The HOMO of the endo and exo transition states are shown below. As expected, the endo HOMO is lower in energy than the exo HOMO. Both HOMOs are antisymmetric with respect to the plane. It is interesting to see that there is an absence of MO lobes around the -(C=O)-O-(C=O)- fragment. This is not the expected outcome of the secondary orbital overlap effect, since the SOO predicts that bonding interactions exist between the -(C=O)-O-(C=O)- fragment and the newly forming double bond. This suggests that either (a) the computational methods used to visualise these orbitals are not accurate enough, or that (b) the secondary orbital overlap is a useful way of rationalising the favoured formation of the endo product, but its validity is questionable.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

The table below summarises key C-C bond lengths in the endo and exo transition states. This includes directly bonded carbons and through space interactions of carbons.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

The partly formed σ C-C bonds have nearly the same distance in both endo and exo structures. In both structures the C3-C4 and C5-C6 bond lenghts are slightly longer than that of a typical C=C double bond (1.33 Å), indicating that the C3-C4 and C5-C6 bonds are reacting to form single bonded carbons. The C4-C5 bond is shorter than that of a typical C-C single bond (1.52 Å), which indicates that a double bond is forming.

The C1-C4/ C8-C5 through space distance in the endo product is shorter than the C1-C9/ C8-C10 interaction in the exo product. The shorter distance (i.e. larger strain) in the endo product is a trade off for the favourable secondary orbital overlap interactions observed in the transition state.

= References =

<references/>

Rep:Mod:maw210

2012-12-07T16:47:35Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. This is consistent with the obtained calculations: The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, but the endo TS has a slightly lower energy than the exo TS, hence the endo structure is kinetically favoured.

The HOMO of the endo and exo transition states are shown below. As expected, the endo HOMO is lower in energy than the exo HOMO. Both HOMOs are antisymmetric with respect to the plane. It is interesting to see that there is an absence of MO lobes around the -(C=O)-O-(C=O)- fragment. This is not the expected outcome of the secondary orbital overlap effect, since the SOO predicts that bonding interactions exist between the -(C=O)-O-(C=O)- fragment and the newly forming double bond. This suggests that either (a) the computational methods used to visualise these orbitals are not accurate enough, or that (b) the secondary orbital overlap is a useful way of rationalising the favoured formation of the endo product, but its validity is questionable.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

The table below summarises key C-C bond lengths in the endo and exo transition states. This includes directly bonded carbons and through space interactions of carbons.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

The partly formed σ C-C bonds have nearly the same distance in both endo and exo structures. In both structures the C3-C4 and C5-C6 bond lenghts are slightly longer than that of a typical C=C double bond (1.33 Å), indicating that the C3-C4 and C5-C6 bonds are reacting to form single bonded carbons. The C4-C5 bond is shorter than that of a typical C-C single bond (1.52 Å), which indicates that a double bond is forming.

The C1-C4/ C8-C5 through space distance in the endo product is shorter than the C1-C9/ C8-C10 interaction in the exo product. The shorter distance (i.e. larger strain) in the endo product is a trade off for the favourable secondary orbital overlap interactions observed in the transition state.

= References =

<references/>

Rep:Mod:maw210

2012-12-07T16:44:40Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. This is consistent with the obtained calculations: The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, but the endo TS has a slightly lower energy than the exo TS, hence the endo structure is kinetically favoured.

The HOMO of the endo and exo transition states are shown below. As expected, the endo HOMO is lower in energy than the exo HOMO. Both HOMOs are antisymmetric with respect to the plane. It is interesting to see that there is an absence of MO lobes around the -(C=O)-O-(C=O)- fragment. This is not the expected outcome of the secondary orbital overlap effect, since the SOO predicts that bonding interactions exist between the -(C=O)-O-(C=O)- fragment and the newly forming double bond. This suggests that either (a) the computational methods used to visualise these orbitals are not accurate enough, or that (b) the secondary orbital overlap is a useful way of rationalising the favoured formation of the endo product, but its validity is questionable.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

The table below summarises key C-C bond lengths in the endo and exo transition states. This includes directly bonded carbons and through space interactions of carbons.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

The partly formed σ C-C bonds have nearly the same distance in both endo and exo structures. In both structures the C3-C4 and C5-C6 bond lenghts are slightly longer than that of a typical C=C double bond (1.33 Å), indicating that the C3-C4 and C5-C6 bonds are reacting to form single bonded carbons. The C4-C5 bond is shorter than that of a typical C-C single bond (1.52 Å), which indicates that a double bond is forming.

The C1-C4/ C8-C5 through space distance in the endo product is shorter than the C1-C9/ C8-C10 interaction in the exo product. The shorter distance in the endo product is a trade off for the favourable secondary orbital overlap interactions observed in the transition state.

= References =

<references/>

Rep:Mod:maw210

2012-12-07T16:42:10Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. This is consistent with the obtained calculations: The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, but the endo TS has a slightly lower energy than the exo TS, hence the endo structure is kinetically favoured.

The HOMO of the endo and exo transition states are shown below. As expected, the endo HOMO is lower in energy than the exo HOMO. Both HOMOs are antisymmetric with respect to the plane. It is interesting to see that there is an absence of MO lobes around the -(C=O)-O-(C=O)- fragment. This is not the expected outcome of the secondary orbital overlap effect, since the SOO predicts that bonding interactions exist between the -(C=O)-O-(C=O)- fragment and the newly forming double bond. This suggests that either (a) the computational methods used to visualise these orbitals are not accurate enough, or that (b) the secondary orbital overlap is a useful way of rationalising the favoured formation of the endo product, but its validity is questionable.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

The table below summarises key C-C bond lengths in the endo and exo transition states. This includes directly bonded carbons and through space interactions of carbons.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

The partly formed σ C-C bonds have nearly the same distance in both endo and exo structures. In both structures the C3-C4 and C5-C6 bond lenghts are slightly longer than that of a typical C=C double bond (1.33 Å), indicating that the C3-C4 and C5-C6 bonds are reacting to form single bonded carbons. The C4-C5 bond is shorter than that of a typical C-C single bond (1.52 Å), which indicates that a double bond is forming.

= References =

<references/>

Rep:Mod:maw210

2012-12-07T16:34:22Z

Maw210: /* Exo Product */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. This is consistent with the obtained calculations: The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, but the endo TS has a slightly lower energy than the exo TS, hence the endo structure is kinetically favoured.

The HOMO of the endo and exo transition states are shown below. As expected, the endo HOMO is lower in energy than the exo HOMO. Both HOMOs are antisymmetric with respect to the plane. It is interesting to see that there is an absence of MO lobes around the -(C=O)-O-(C=O)- fragment. This is not the expected outcome of the secondary orbital overlap effect, since the SOO predicts that bonding interactions exist between the -(C=O)-O-(C=O)- fragment and the newly forming double bond. This suggests that either (a) the computational methods used to visualise these orbitals are not accurate enough, or that (b) the secondary orbital overlap is a useful way of rationalising the favoured formation of the endo product, but its validity is questionable.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

The table below summarises key C-C bond lengths in the endo and exo transition states. This includes directly bonded carbons and through space interactions.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T16:33:19Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. This is consistent with the obtained calculations: The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, but the endo TS has a slightly lower energy than the exo TS, hence the endo structure is kinetically favoured.

The HOMO of the endo and exo transition states are shown below. As expected, the endo HOMO is lower in energy than the exo HOMO. Both HOMOs are antisymmetric with respect to the plane. It is interesting to see that there is an absence of MO lobes around the -(C=O)-O-(C=O)- fragment. This is not the expected outcome of the secondary orbital overlap effect, since the SOO predicts that bonding interactions exist between the -(C=O)-O-(C=O)- fragment and the newly forming double bond. This suggests that either (a) the computational methods used to visualise these orbitals are not accurate enough, or that (b) the secondary orbital overlap is a useful way of rationalising the favoured formation of the endo product, but its validity is questionable.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

The table below summarises key C-C bond lengths in the endo and exo transition states. This includes directly bonded carbons and through space interactions.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T16:31:17Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. This is consistent with the obtained calculations: The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, but the endo TS has a slightly lower energy than the exo TS, hence the endo structure is kinetically favoured.

The HOMO of the endo and exo transition states are shown below. As expected, the endo HOMO is lower in energy than the exo HOMO. Both HOMOs are antisymmetric with respect to the plane. It is interesting to see that there is an absence of MO lobes around the -(C=O)-O-(C=O)- fragment. This is not the expected outcome of the secondary orbital overlap effect, since the SOO predicts that bonding interactions exist between the -(C=O)-O-(C=O)- fragment and the newly forming double bond. This suggests that either (a) the computational methods used to visualise these orbitals are not accurate enough, or that (b) the secondary orbital overlap is a useful way of rationalising the favoured formation of the endo product, but its validity is yet to be determined.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T16:17:08Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. This is consistent with the obtained calculations: The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, but the endo TS has a slightly lower energy than the exo TS, hence the endo structure is kinetically favoured.

The HOMO of the endo and exo transition states are shown below. As expected, the endo HOMO is lower in energy than the exo HOMO. Both HOMOs are antisymmetric with respect to the plane. It is interesting to see that there is an absence of MO lobes around the -(C=O)-O-(C=O)- fragment. This is not the expected outcome of the secondary orbital overlap effect, since the SOO predicts that bonding interactions exist between the -(C=O)-O-(C=O)- fragment and the newly forming double bond. This suggests that either (a) the computational methods used to visualise these orbitals were insufficient, or that (b) the secondary orbital overlap is a useful way to rationalise the favoured formation of the endo product, but its validity is yet to be determined.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T16:11:35Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. This is consistent with the obtained calculations: The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, but the endo TS has a slightly lower energy than the exo TS, hence the endo structure is kinetically favoured.

The HOMO of the endo and exo transition states are shown below. As expected, the endo HOMO is lower in energy than the exo HOMO. Both HOMOs are antisymmetric with respect to the plane. It is interesting to see that there is an absence of MO lobes around the -(C=O)-O-(C=O)- fragment, especially in the endo HOMO. This is not the expected outcome of the secondary orbital overlap effect, since the SOO predicts that there are bonding interactions between the -(C=O)-O-(C=O)- fragment and the newly forming double bond.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:50:15Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. This is consistent with the obtained calculations: The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, but the endo TS has a slightly lower energy than the exo TS, hence the endo structure is kinetically favoured.

The HOMO of the endo and exo transition states are plotted below. As expected, the endo HOMO is lower in energy than the exo HOMO

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:47:47Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. This is consistent with the obtained calculations: The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, but the endo TS has a slightly lower energy than the exo TS, hence the endo structure is kinetically favoured.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:47:19Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. This is consistent with the obtained calculations: The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, but the endo TS has a slightly lower energy than the exo TS, hence the endo structure is kinetically favoured.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:45:53Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional non-bonding π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond. As a result the energy of the endo TS is lowered and the endo product forms faster. The energy of the endo TS is -32.3 kcal mol-1 and the energy of the exo TS is -31.6 kcal mol-1. The energies are very close, however the endo TS has a slightly lower energy than the exo TS.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:38:52Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the maleic anhydride reacts with its O atom facing toward the diene, additional π-interactions can occur between the p orbitals on the carbonyl carbons and that of the carbon atoms forming the new double bond.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:34:11Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich Cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps. Because the

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo maw.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

= References =

<references/>

File:Endo homo maw.PNG

2012-12-07T15:33:57Z

Maw210:

Rep:Mod:maw210

2012-12-07T15:22:59Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they react to form the endo/ exo product. In both cases the electron rich Cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:22:04Z

Maw210: /* Comparison of Endo and Exo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product. In both cases the electron rich Cyclohexa-1,3-diene HOMO donates electrons into the electron deficient maleic anhydride LUMO.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

The Endo TS has two sets of favourable interactions: the primary and secondary orbital overlaps.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:16:08Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Endo and Exo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:13:43Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:13:27Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= -0.34274]]
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:13:12Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Exo homo1.PNG|thumb|300px|Exo HOMO (E= 34274]]
|}

= References =

<references/>

File:Exo homo1.PNG

2012-12-07T15:12:26Z

Maw210:

Rep:Mod:maw210

2012-12-07T15:10:46Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO of Endo/ Exo product '''
! scope="row" style="text-align: left;"| [[File:Endo homo.PNG|thumb|300px|Endo HOMO (E= -0.34504)]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Exo HOMO (E= ]]
|}

= References =

<references/>

File:Endo homo.PNG

2012-12-07T15:09:53Z

Maw210: uploaded a new version of "File:Endo homo.PNG"

Rep:Mod:maw210

2012-12-07T15:03:57Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|210px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:03:47Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|220px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:02:43Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|230px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:01:35Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|250px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:01:01Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|300px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T15:00:38Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts1.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|200px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

File:Endo ts1.png

2012-12-07T15:00:22Z

Maw210:

Rep:Mod:maw210

2012-12-07T14:50:16Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts2.png|thumb|200px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

File:Exo ts2.png

2012-12-07T14:49:59Z

Maw210:

Rep:Mod:maw210

2012-12-07T14:47:03Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts1.png|thumb|200px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

File:Exo ts1.png

2012-12-07T14:46:49Z

Maw210:

File:Exo ts.png

2012-12-07T14:45:37Z

Maw210: uploaded a new version of "File:Exo ts.png"

Rep:Mod:maw210

2012-12-07T14:39:43Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts.png|thumb|200px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T14:39:17Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts.png|thumb|300px]]
! style="text-align: centre;"|[[File:Exo ts.png|thumb|300px]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

File:Exo ts.png

2012-12-07T14:38:49Z

Maw210: uploaded a new version of "File:Exo ts.png"

Rep:Mod:maw210

2012-12-07T14:35:38Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="0" style="border-collapse:collapse;" align="center"
! scope="row" style="text-align: left;"| [[File:Endo ts.png|thumb|300px]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

File:Endo ts.png

2012-12-07T14:34:45Z

Maw210: uploaded a new version of "File:Endo ts.png"

Rep:Mod:maw210

2012-12-07T14:20:07Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

The following diagram shows the overlap of the reactant molecules and how they lead to the endo/ exo product.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T14:15:24Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | 2.17
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 2.95
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 1.49
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | 1.40
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | 1.39
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T14:10:22Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | 2.16
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | ''' '''
|-
| width="125" align="center" | '''C1-C4/ C8-C5''' (through space)
| align="center" | 2.89
| width="125" align="center" | '''C1-C9/ C8-C10''' (through space)
| align="center" | 33.16
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 1.49
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 41.32
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | 1.40
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | ''' '''
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | 1.39
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | ''' '''
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T13:59:41Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | ''' '''
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | ''' '''
|-
| width="125" align="center" | '''C1-C5/ C8-C4''' (through space)
| align="center" | 44.69
| width="125" align="center" | '''C1-C10/ C8-C9''' (through space)
| align="center" | 33.16
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 54.76
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 41.32
|-
| width="125" align="center" | ''' C4-C5 '''
| width="125" align="center" | ''' '''
| width="125" align="center" | ''' C4-C5'''
| width="125" align="center" | ''' '''
|-
| width="125" align="center" | ''' C3-C4/ C5-C6 '''
| width="125" align="center" | ''' '''
| width="125" align="center" | ''' C3-C4/ C5-C6'''
| width="125" align="center" | ''' '''
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T13:53:42Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="2"|[[File:Endo geom.png|250px]]
!colspan="2"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | ''' '''
| width="125" align="center" | ''' C2-C3/ C6-C7'''
| width="125" align="center" | ''' '''
|-
| width="125" align="center" | '''C1-C5/ C8-C4'''
| align="center" | 44.69
| width="125" align="center" | '''C1-C10/ C8-C9'''
| align="center" | 33.16
|-
| width="125" align="center" | ''' C1-C2/ C7-C8 '''
| align="center" | 54.76
| width="125" align="center" | '''C1-C2/ C7-C8'''
| align="center" | 41.32
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T13:45:32Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="3"|[[File:Endo geom.png|250px]]
!colspan="3"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | ''' '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' C2-C3/ C6-C7 '''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''C-C'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''C-C'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

= References =

<references/>

Rep:Mod:maw210

2012-12-07T13:44:47Z

Maw210: /* Comparison of Exo and Endo */

= Computational Lab, Module 3 =

'''Maya A Wright'''

Computational chemistry is a useful tool in investigating key properties of a molecule such as structure, dipole moment, energy, vibrational modes, and reactivity. In this module we seek to gain insight into the transition states of two well-known chemical reactions: The Cope Rearrangement and the Diels-Alder reaction. GaussView 5.0 was used for all calculations.

= The Cope Rearrangement =

The Cope Rearrangement is a pericyclic reaction in which a 1,5-diene rearranges in a [3,3]-sigmatropic fashion. In this module the rearrangement of 1,5-hexadiene is studied.

[[File:Cope1 reaction.png|center|250px]]

To determine the mechanism of the reaction it is necessary to consider the different conformations of 1,5-hexadiene. There are six possible gauche conformations and four possible anti conformations that the 1,5-hexadiene can adopt. The energy and symmetry of each conformation was determined by optimising each molecule on GaussView 5.0.

The nature of the transition state was determined by conducting a transition state optimisation on the anti 2 conformation of 1,5-hexadiene. Different methods were employed to investigate both the chair and boat conformations. The vibrational frequency and energy of each transition state was calculated and compared.

[[File:chair-boat-ts.png|center|250px]]

== Conformations of 1,5-hexadiene ==

=== Optimisation of 1,5-hexadiene conformers, HF/3-21G basis set ===

The HF/3-21G basis set was used to optimise ten possible conformations of 1,5-hexadiene. The following table summarises the energy and point groups of the possible conformations of 1,5-hexadiene.

{| class="wikitable" "border="1"
|+ Conformations of 1,5-hexadiene
!Conformer
!width="200px"|Structure
!Point Group !! Energy (a.u.) !! Relative Energy (kcal mol-1) !! Optimisation File !! Summary Table
|-
|-
| gauche 1 || [[File:Gauche1 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche1 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.68772 || 3.10 || [[Media:HEXADIENE GAUCHE1 321G.LOG| Gauche 1]] || [[File:Gauche1 sum maw.PNG|200px]]
|-
|-
| gauche 2 || [[File:Gauche2.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE2 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 2 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69167 || 0.62 || [[Media:HEXADIENE GAUCHE2 OPT.LOG| Gauche 2]] || [[File:Gauche2 sum.PNG|200px]]
|-
| gauche 3 || [[File:Gauche3 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE GAUCHE3 OPT.mol</uploadedFileContents>
<text> Click for optimised gauche 3 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69266 || 0.00 || [[Media:HEXADIENE GAUCHE3 OPT.LOG| Gauche 3]] || [[File:Gauche3 sum.PNG|200px]]
|-
| gauche 4 || [[File:Gauche4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche4 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 4 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69153 || 0.71 || [[Media:HEXADIENE GAUCHE4 321G.LOG| Gauche 3]] || [[File:Gauche4 sum.PNG|200px]]
|-
| gauche 5 || [[File:Gauche5 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche5 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 5 </text>
</jmolAppletButton>
</jmol>
|| C1|| -231.68962 || 1.91 || [[Media:HEXADIENE GAUCHE5 321G.LOG| Gauche 5]] || [[File:Gauche5 sum.PNG|200px]]
|-
| gauche 6 || [[File:Gauche6 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene gauche6 321G.mol</uploadedFileContents>
<text> Click for optimised gauche 6 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.68916 || 2.20 || [[Media:HEXADIENE GAUCHE6 321G.LOG| Gauche 6]] || [[File:Gauche6 sum.PNG|200px]]
|-
| anti 1 || [[File:Anti1 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI1 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 1 </text>
</jmolAppletButton>
</jmol>
|| C2 || -231.69260 || 0.04 || [[Media:HEXADIENE ANTI1 OPT.LOG| Anti 1]] || [[File:Anti1 sum.PNG|200px]]
|-
| anti 2 || [[File:Anti2 pic.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>HEXADIENE ANTI2 OPT.mol</uploadedFileContents>
<text> Click for optimised anti 2</text>
</jmolAppletButton>
</jmol>
|| Ci || -231.69254|| 0.08 || [[Media:HEXADIENE ANTI2 OPT.LOG| Anti 2]] || [[File:Anti2 sum.PNG|200px]]
|-
| anti3 || [[File:Anti3 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti3 321G.mol</uploadedFileContents>
<text> Click for optimised anti 3 </text>
</jmolAppletButton>
</jmol>
|| C2h || -231.68907 || 2.25 || [[Media:HEXADIENE ANTI3 321G.LOG| Anti 3]] || [[File:Anti3 sum.PNG|200px]]
|-
| anti4 || [[File:Anti4 maw.PNG|200px]]
<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti4 321G.mol</uploadedFileContents>
<text> Click for optimised anti 4 </text>
</jmolAppletButton>
</jmol>
|| C1 || -231.69097 || 1.06 || [[Media:HEXADIENE ANTI4 321G.LOG| Anti 4]] || [[File:Anti4 sum.PNG|200px]]
|-
|}

'''Analysis'''

One would expect the lowest energy conformer of 1,5-hexadiene to be one of the anti conformers, since this would have the pi bonded groups as far apart from each other as possible, thus lowering the steric repulsion. However from the above table it is apparent that the lowest energy conformer is the gauche3 molecule. This is due to favourable interactions between the pi electrons of the double bond and the nearby vinyl hydrogen atom <ref> Brandon C. et. al., ''MOLECULAR PHYSICS'', '''2002''', ''100'', 4, 441-446 </ref>.

=== Optimisation of 1,5-hexadiene (anti 2), 6-31G(d) basis set ===

The anti 2 conformer was reoptimised using a more accurate basis set (DFT, 6-31G(d)).

The optimisation file is liked to [[Media:HEXADIENE ANTI2 OPT 631GD.LOG| here]]

<jmol>
<jmolAppletButton>
<uploadedFileContents>Hexadiene anti2 opt 631Gd.mol</uploadedFileContents>
<text> Click for optimised molecule </text>
</jmolAppletButton>
</jmol>

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Anti 2 Reoptimisation '''
! scope="row" style="text-align: left;"| [[File:Anti2 pic 631G.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Anti2 sum 631G.PNG|thumb|200px|Summary]]
|}

=== Comparison of HF/3-21G and 6-31G(d) optimised anti 2 conformer ===

{| border="1" style="border-collapse:collapse;" align="center"
|+ '''''Comparison of bond lengths/ Bond angles for different basis sets'''''
! colspan="6" style="text-align: centre;"| [[File:Geometry.png|300px]]
|-
! colspan="3" style="text-align: left;"| Bond Length (Å) || ! colspan="3" style="text-align: left;"| Bond Angle
|-
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
! style="text-align: left;"|  
! style="text-align: left;"| HF/3-21G
! style="text-align: left;"| 6-31G(d)
|-
| style="text-align: left;"| C1-C2
| style="text-align: left;"| 1.316
| style="text-align: left;"| 1.334
| style="text-align: left;"| C1-C2-C3
| style="text-align: left;"| 124.8º
| style="text-align: left;"| 125.3º
|-
| style="text-align: left;"| C2-C3
| style="text-align: left;"|1.509
| style="text-align: left;"| 1.504
| style="text-align: left;"|C2-C3-C4
| style="text-align: left;"| 111.3º
| style="text-align: left;"| 112.7º
|-
| style="text-align: left;"| C3-C4
| style="text-align: left;"| 1.553
| style="text-align: left;"| 1.548
| style="text-align: left;"| C1-C2-C3-C4 (dihedral)
| style="text-align: left;"| 114.7º
| style="text-align: left;"| 118.6º
|-
|}

The bond lengths do not change significantly with the basis set used, although the 6-31G(d) bond lengths are slightly shorter overall than the 3-21G bond lengths. The maximum change in bond length was about 1.4%. The 6-31G(d) calculations yielded larger bond angles than the 3-21G calculations. The C1-C2-C3-C4 dihedral angle increased by 3.4% in going from 3-21G to 6-31G(d). These changes in bond length and bond angle are negligible, so the geometry has not changed significantly in going from the 3-21G to 6-31G(d) basis set.

=== Frequency Analysis of anti2 1,5-hexadiene (6-31G(d)) ===

A frequency analysis was conducted on the B3LYP/6-31G(d) optimised anti 2 conformer. All vibrational frequencies are real and positive, thus the obtained structure is a minimum.

The optimisation file is liked to [[Media:HEXADIENE ANTI2 FREQ 631GD.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frequency Analysis of anti 2 '''
! scope="row" style="text-align: left;"| [[File:Freq sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:IR anti2 maw.PNG|300px|thumb|IR Spectrum]]
! style="text-align: centre;"|[[File:Hexadiene anti2 631g(d) freq.PNG|thumb|150px|'''List of 42 Vibrational Frequencies''']]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Selected Vibrational Modes (Click to view animation) '''
! scope="row" style="text-align: left;"| [[File:Vib maw.gif|thumb|300px|940 cm-1, intensity = 60.9]]
! style="text-align: centre;"|[[File:Vib2 maw.gif|300px|thumb|1734 cm-1, Intensity = 18.1]]
! style="text-align: centre;"|[[File:Vib3 maw.gif|thumb|300px|3234 cm-1, Intensity = 45.5]]
|}

'''Thermochemistry'''

The energy of the molecule is dependent on parameters such as the enthalpy, entropy, free energy and temperature. The following table summarises this:

<pre> Zero-point correction= 0.142507 (Hartree/Particle)
Thermal correction to Energy= 0.149853
Thermal correction to Enthalpy= 0.150797
Thermal correction to Gibbs Free Energy= 0.110933
(1) Sum of electronic and zero-point Energies= -234.469204
(2) Sum of electronic and thermal Energies= -234.461857
(3) Sum of electronic and thermal Enthalpies= -234.460913
(4) Sum of electronic and thermal Free Energies= -234.500777
</pre>

(1) corresponds to the energy of the molecule at 0 K, which includes the zero-point energy. (2) is the energy of the molecule at 298.15K. This takes into account the translational, rotational, and vibrational energies. (3) corrects for the thermal energy available at room temperature, E= H + RT. (4) accounts for the entropic contribution from the free energy<ref> Module 3 Laboratory Script </ref>, G = H - TS

=== Frequency analysis of anti2 1,5-hexadiene (HF/3-21G) ===

A frequency calculation was done for the anti 2 conformer using the 3-21G basis set in order to obtain thermochemical information. (Later used to calculate the activation energy of the cope rearrangement via the chair and boat transition states).

The optimisation file is linked to [[Media:ANTI2 FREQ 321G.LOG|here]]

<pre> Zero-point correction= 0.152996 (Hartree/Particle)
Thermal correction to Energy= 0.159970
Thermal correction to Enthalpy= 0.160914
Thermal correction to Gibbs Free Energy= 0.121620
Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532565
Sum of electronic and thermal Enthalpies= -231.531621
Sum of electronic and thermal Free Energies= -231.570916 </pre>

== Chair Transition State ==

Three different computational methods were used to determine the structure and imaginary vibrational frequency of the chair transition state: (a) The Berny TS Optimisation (b) The Frozen Coordinates Method, and (c) The IRC Method.

Optimisation of a transition state can be difficult. The input structure must be relatively close to the true transition state structure, which corresponds to a saddle point on the potential energy surface <ref> Lewars, E., ''Computational Chemistry'', Springer, London, p.17 </ref>. If the starting structure is too far off, the calculation may not follow the direction of the reaction coordinate.

The Berny TS Optimisation method allows for the calculation of a local energy minimum on the potential energy surface. This is done by computing the Hessian matrix, i.e. the second derivative force matrix, at every point on the reaction coordinate<ref> http://www.chem.cornell.edu/dbc6/documents/Gaussian_optimization.pdf </ref>. Since an exact calculation of the Hessian matrix takes too long, GaussView uses approximate Hessian matrices instead. For this to work the starting structure must resemble the true structure.

In the Frozen Coordinates method the distance between the terminal carbon atoms is fixed while the rest of the molecule is optimised. Unlike the Berny TS method, after the molecule has been optimised it is not necessary to calculate the Hessian for every point. Instead, the terminal carbon distance is unfrozen and the derivative is taken along the reaction coordinate until it reaches a minimum.

The IRC (or Intrinsic Reaction Coordinate) method allows for us to follow the minimum energy pathway of a reaction. This requires the initial force constants<ref>http://www.gaussian.com/g_tech/g_ur/k_irc.htm</ref>, so the calculation is based on the Berny optimised TS structure. The calculation proceeds in the direction with the steepest slope on the potential energy surface.

=== Optimisation of an allyl fragment (HF/3-21G) ===

As a first step to computing the transition structure, an allyl fragment was optimised. The optimisation file is liked to [[Media:ALLYL MAW OPT.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Allyl Optimisation '''
! scope="row" style="text-align: left;"| [[File:Allyl opt maw pic.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Allyl opt maw.PNG|thumb|200px|Summary]]
|}

=== Berny Optimisation of the chair transition state (HF/3-21G) ===

The HF/3-21G optimised allyl fragment was used to construct a 'guess' chair transition state structure. The guess structure was arranged with the terminal carbon atoms approximately 2.2 Å apart. The Job Type was set to Opt+Freq/ Optimise to a TS (Berny). The force constants were calculated 'Once' and the words 'Opt=NoEigen' were added to the additional keywords box in order to stop the calculation from crashing in case more than one imaginary frequency was computed.

The optimisation file is liked to [[Media:CHAIR TS BERNY MAW.LOG| here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Berny Optimisation '''
! scope="row" style="text-align: left;"| [[File:Chair ts berny maw pic.PNG|thumb|250px|Summary]]
! style="text-align: centre;"|[[File:Chair ts berny maw.gif|thumb|250px|Optimised Molecule]]
|}

The imaginary frequency occurs at 818 cm-1. This clearly resembles the Cope rearrangement as the terminal C atoms oscillate toward and then away from each other. One can imagine a bond forming between the terminal C atoms as they approach each other, and then breaking as they move away from each other.

'''Bond forming/ breaking length''': 2.02 Å

=== Optimisation of chair transition state: Frozen Coordinates Method (HF/3-21G) ===

The chair transition state was optimised using the frozen coordinates method. First, the terminal C-C bond lengths were frozen to 2.2 Å while the rest of the molecule was optimised using the HF/3-21G basis set (Keywords: Opt=modredundant). Then the terminal bond lengths were unfrozen and the derivative was taken along the path with the steepest slope on the potential energy surface. The results of the second calculation are given below:

The optimisation file is linked to [[Media:OPT FREQ 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Frozen coord sum.PNG|thumb|200px|Summary]]
! style="text-align: centre;"|[[File:Frozen coord freq.gif|thumb|200px|Vibrational mode]]
|}

The imaginary frequency occurs at 818 cm-1 which is in agreement with the Berny TS optimisation method.

'''Bond forming/ breaking length''': 2.02 Å

The bond forming/ bond breaking bond length is the same as that calculated by the Berny TS optimisation. It is smaller than the initial guess of 2.2 Å. The energies for the Berny TS and Frozen Coordinates optimised molecules are also the same at -231.619322 a.u. The fact that the vibrational frequency, bond forming/ bond breaking length, and the energies of the two molecule are in good agreement shows that the two strucutres are very similar.

=== Optimisation of chair transition state: IRC Method (HF/3-21G) ===

The minimum energy pathway of the reaction was followed using the Intrinsic Reaction Coordinate method. The previously optimised berny transition state structure was used for the input file. 50 iterations were taken and the reaction coordinate was computed only in the forward direction.

The optimisation file is linked to [[Media:IRC 1 MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''First Iteration (no. 1)'''
! scope="row" style="text-align: left;"| [[File:IRC 1st it.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[Image:IRC 1st it sum.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Last Iteration (no. 44) '''
! scope="row" style="text-align: left;"| [[File:Last iteration maw.PNG|thumb|200px|Structure]]
! style="text-align: centre;"|[[File:Irc last iteration sum.PNG|thumb|200px|Summary]]
|}

[[File:IRC movie maw.gif|thumb|center|300px|'''Animation''']]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' RMS Gradient Graphs '''
! scope="row" style="text-align: left;"| [[File:Irc opt maw.PNG|thumb|500px|(1) Total Energy along IRC]]
! style="text-align: centre;"|[[File:Irc opt maw 1.PNG|thumb|500px|(2) RMS Gradient Norm along IRC]]
|}

Graph (1) maps the energy of the molecule as a function of optimisation step number. As the optimisation progresses, the energy of the molecules approaches a constant value. This shows that the calculation is approaching a minimum geometry. However on inspection of graph (2) it is apparent that the RMS gradient has not quite reached zero in the last step. Thus a further optimisation must be carried out.

'''Second optimisation'''

A further optimisation was carried out on the last IRC structure (no. 44) in order to ensure that an energy minimum was reached. The 44th structure was optimised to a minimum.

The optimisation file is linked to [[Media:IRC MINIMISATION FINAL MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Reoptimisation of last iteration in IRC'''
! scope="row" style="text-align: left;"| [[File:Irc opt final maw pic.PNG|thumb|left|200px|Optimised structure]]
! style="text-align: centre;"|[[Image:Irc opt final maw sum.PNG|200px|Summary]]
|}

=== Optimisation of chair transition state using 6-31G(d) basis set ===

The Berny optimised chair transition state (HF/3-21G) was reoptimised using a higher accuracy 6-31G(d) basis set. A frequency analysis was also conducted.

The optimisation file is linked to [[Media:CHAIR TS BERNY 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised chair transition state '''
! scope="row" style="text-align: left;"| [[File:Chair ts 631G.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Chair opt 631G sum.PNG|thumb|200px|Summary]]
|}

== Boat Transition State ==

=== Optimisation of boat transition state- QST2 ===

The boat TS was optimised using the QST2 method. This method requires the input of a reactant and product structure so that the calculation can flit between the two structures in order to find the transition state. The reactant and product molecules were arranged so that their geometries resembled that of the boat transition state. The C2-C3-C4-C5 dihedral angle was set to 0° and the C2-C3-C4 and C3-C4-C5 inner angles were set to 100°. The reactant and product molecules were numbered so that their connectivity resembled that of the cope rearrangement.

[[File:Reactant product frozen.PNG|thumb|center|400px|Numbered reactant and product (1,5-hexadiene)]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ '''Optimised boat structure and summary'''
! scope="row" style="text-align: left;"| [[File:Boat opt maw.PNG|thumb|250px|Optimised structure]]
! style="text-align: centre;"|[[Image:Boat sum maw.PNG|thumb|250px|Summary]]
|}

The optimisation file is linked to [[Media:BOAT TS OPT2 QST2 MAW.LOG|here]]

'''Vibrational Frequency'''

The optimised boat structure has one imaginary frequency at -840 cm-1

[[File:Boat opt freq maw.gif|thumb|center|300px|click to view animation]]

=== Optimisation of boat transition state using 6-31G(d) basis set ===

The HF/3-21G optimised boat transition state was reoptimised using a higher accuracy 6-31G(d) basis set.

The optimisation file is linked to [[Media:BOAT TS OPT 631G MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' 6-31G(d) optimised boat transition state '''
! scope="row" style="text-align: left;"| [[File:Boat ts 631G pic.PNG|thumb|200px|Transition State]]
| style="text-align: centre;"|[[File:Boat ts 631G sum.PNG|thumb|200px|Summary]]
|}

== Comparison of 3-21G and 6-31G(d) optimised reactant and transition state structures ==

By visual inspection of the optimised reactant/ transition state molecules in the above sections, the geometries of the molecules do not change significantly with the basis set used. However, there is a notable difference in energy between the two levels of theory, with the 6-31G(d) basis set predicting the existance of lower energy reactants and transition states. The energies of the reactants and transition states for each level of theory is compared in the table below.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ ''' Energy summary (a.u.) '''
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G(d)'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies (0 K)'''
| width="125" align="center" | '''Sum of electronic and thermal energies (298.15 K)'''
|-
| '''Chair TS'''
| align="center" | -231.619322
| align="center" | -231.466706
| align="center" | -231.461345
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.602802
| align="center" | -231.450930
| align="center" | -231.445302
| align="center" | -234.543093
| align="center" | -234.402339
| align="center" | -234.396006
|-
| '''Reactant (anti2)'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532565
| align="center" | -234.611710
| align="center" | -234.469204
| align="center" | -234.461857
|}

The activation energy for the Cope Rearrangement was calculated by taking the difference between the transition state and reactant molecule energies at 0 K and 298.15 K. These values are compared to experimentally determined activation energies.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Activation Energy Summary (kcal mol-1)'''
|-
| ''' '''
!colspan="2"|'''HF/3-21G'''
!colspan="2"|'''B3LYP/6-31G(d)'''
| width="125" align="center" | '''Experimental<ref>Module 3 Laboratory Script</ref>'''
|-
| ''' '''
| width="125" align="center" | ''' 0 K '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' 0 K'''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''ΔEa Chair'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔEa Boat'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

The calculated activation energies at 0 K for the higher accuracy basis set (6-31G(d)) gives a closer match to the experimental data for both the chair and boat conformations. Also, the chair transition state is predicted to have a lower activation energy than the boat transition state. Thus, one may be led to think that the reaction proceeds via the chair transition state. However, there is still much controversy on whether this is true. One definite conclusion is that the computed transition state vibrations show the reaction occurring in a concerted fashion. The dotted lines show that the electrons involved in the reaction are delocalised and that they are not fixed between any two atoms. Thus it is likely that the mechanism for the cope rearrangement is concerted and goes via either a chair or boat transition state.

= The Diels-Alder Reaction =

The Diels-Alder reaction is a pericyclic reaction in which a diene reacts with an alkene (dienophile) in a concerted fashion. The reaction is successful because of the matching orbital symmetry of the diene HOMO/dienophile LUMO and vice versa. The p orbitals of each reactant overlap head on to form two new σ bonds via a stable, aromatic transition state.

[[File:Diels alder homo lumo.png|center|350px]]

In the first section we compute the HOMO and LUMO of butadiene in order to gain insight into the frontier orbitals that are key to the Diels-Alder reaction. We then go on to investigate the reaction of ethylene and butadiene.

[[File:Diels-alder maw.png|center|250px]]

The transition state of the reaction is computed and its mechanism is discussed.

Finally, we explore the Diels-Alder reaction between Cyclohexa-1,3-diene and maleic anhydride in which there are two possible products: a kinetically stable endo product and a thermodynamically stable exo product.

== Butadiene ==

=== AM1 semi-emperical optimisation of cis-butadiene ===

The geometry of cis-butadiene was optimised using the AM1 semi-empirical method.

The optimisation file is linked to [[Media:BUTADIENE OPT MAW.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Geometry optimisation of cis-butadiene'''
! scope="row" style="text-align: left;"| [[File:Butadiene opt pic1.PNG|thumb|250px|Structure]]
| style="text-align: centre;"|[[File:Butadiene opt pic.PNG|thumb|230px|Summary]]
|}

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of cis-butadiene '''
! style="text-align: centre;"|[[File:Mb da2.jpg|thumb|230px|Plane of symmetry<ref> Module 3 Laboratory Script </ref>]]
! scope="row" style="text-align: left;"| [[File:Butadiene lumo maw.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Butadiene lumo2 maw.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

== Ethylene + Butadiene ==

=== Berny optimisation of the transition state ===

The transition state of the reaction of ethylene with butadiene was optimised using the AM1 semi-empirical/ Berny TS method. The interfragment distance between ethylene and butadiene was set to be 2.2 Å in the optimisation, as quoted in literature <ref> Goldstein E.,''J. Am. Chem. Soc''., Vol. 118, No. 25, 1996-6039 </ref>.

The optimisation file is linked to [[Media:DA TS OPT FREQ AM1.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' TS optimisation of the Diels-Alder Reaction'''
! scope="row" style="text-align: left;"| [[File:Da ts pic.PNG|thumb|300px|Structure]]
! style="text-align: centre;"|[[File:Da ts sum.PNG|thumb|230px|Summary]]
|-
! style="text-align: centre;"|[[File:Da ts vib.gif|thumb|300px|Imaginary Frequency at -956 cm-1]]
! style="text-align: centre;"|[[File:Lowest postivie frequency.gif|thumb|270px|Lowest Positive Frequency at 147 cm-1]]
|}

The optimised structure clearly corresponds to the Diels-Alder transition state. There is only one imaginary frequency in the optimisation, and one can visualise bonds forming as the ethylene/ butadiene move toward each other in the vibration and breaking as they move away from each other. The bond forming/ breaking process is synchronous and concerted. The dotted lines indicate that the electrons are delocalised and that the σ bonds have not yet completely formed, a characteristic trait of a transition state. The lowest positive frequency at 147 cm-1 does not show the carbon atoms on ethylene/ butadiene getting closer to each other. The ethylene carbon atoms rock from side to side in the plane of the molecule and so do the butadiene carbon atoms. Since the two reactants do not move toward or away from each other in this positive vibrational mode, it does not correspond to the transition state.

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Summary of bond lengths<ref> Margules, L. ''Structural Chemistry'', Vol. 11, Nos. 2-3, 145- 154 </ref> (Å)'''
|-
| width="125" align="center" |''' sp3 C-C'''
| width="125" align="center" | ''' sp2 C=C '''
| width="125" align="center" | ''' sp3-sp2 C-C '''
| width="125" align="center" | ''' van der Waals radius of C'''
| width="125" align="center" | ''' partly formed σ C-C bond'''
|-
| align="center" | 1.52
| align="center" | 1.33
| align="center" | 1.50
| align="center" | 1.70
| align="center" | 2.12
|}

As the ethylene and butadiene move towards each other in the imaginary vibration, the carbon atoms joined by the dotted lines change from sp2 to sp3 character. However when stationary the partly formed σ C-C bond length is 2.12 Å. This is closer to the sp3 - sp3 C-C bond length (1.52 Å) so the transition state must resemble the products more than the reactants, i.e. the reaction has a late transition state. The partly formed σ C-C bond can also be visualised as two individual C atoms of van der Waals radii 1.70 Å starting to meet within the attractive range of each other so that eventually a bond can be formed between them.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' HOMO and LUMO of TS structure '''
! scope="row" style="text-align: left;"| [[File:Da ts mo.PNG|thumb|230px|HOMO- antisymmetric with respect to plane]]
! style="text-align: centre;"|[[File:Da ts lumo.PNG|thumb|230px|LUMO- symmetric with respect to plane]]
|}

The HOMO of the transition structure is antisymmetric with respect to the plane. In this case it is the HOMO of butadiene that reacts with the LUMO of ethylene to form the frontier orbitals of the transition state. The formation of the TS HOMO can be visualised using the following MO diagram:

[[File:MO diagram maw.png|center|400px]]

The electron rich double bonds of butadiene donate into the electron deficient ethylene LUMO. The reaction is allowed because of the symmetry of the interacting orbitals. Both the HOMO of butadiene and the LUMO of ethylene are '''a''' (antisymmetric) with respect to the plain of symmetry. Thus the HOMO of the product that they form is also '''a''' because reactions in which the reactants and products have the same electron distribution are favoured <ref> http://www.ch.ic.ac.uk/local/organic/pericyclic/ </ref>.

== Kinetic vs Thermodynamic Control ==

Dienes and dienophiles that are appropriately substituted can form stereochemical products. This phenomenon arises because there are two ways in which the dieneophile can approach the diene: facing toward (endo) or away (exo) from the diene. The endo product is the kinetically favoured product as it is formed faster, whereas the exo product is thermodynamically more favoured as it is lower in energy. In this module we investigate the reaction of cyclohexa-1,3-diene with maleic anhydride.

[[File:Endo exo ma.png|650px|center]]
=== Endo Product ===

The endo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file could not be uploaded because it exceeded 2.0 MB.

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Endo vib sum maw.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Endo vib maw.gif|thumb|300px|Vibrational mode at -806 cm-1 (Click for animation)]]
|}

The imaginary frequency occurs at -806 cm-1

=== Exo Product ===

The exo transition state for the reaction of Cyclohexa-1,3-diene and maleic anhydride was optimised using the AM1 semi-empirical/ frozen coordinates method. The terminal C-C bond lengths were set to 2.1 Å.

The optimisation file is linked to [[Media:CYCLOHEXA13DIENE OPT MAW STEP2.LOG|here]]

{| border="0" style="border-collapse:collapse;" align="center"
|+ ''' Frozen Coordinates method '''
! scope="row" style="text-align: left;"| [[File:Cyclohexa13diene sum.PNG|thumb|300px|Summary]]
! style="text-align: centre;"|[[File:Cyclohexa13diene freq maw.gif|thumb|300px|Vibrational mode at -812cm-1]]
|}

The imaginary frequency occurs at -812 cm-1

*Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the -(C=O)-O-(C=O)- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -(C=O)-O-(C=O)- fragment for the endo.
*Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
*Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained?
*Examine carefully the nodal properties of the HOMO between the -(C=O)-O-(C=O)- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

=== Comparison of Exo and Endo ===

{| border="1" cellspacing="0" cellpadding="3" align="center"
|+ '''Key Bond lengths in the endo/exo transition states (Å)'''
|-
!colspan="3"|[[File:Endo geom.png|250px]]
!colspan="3"|[[File:Exo geom.png|250px]]
|-
| width="125" align="center" | ''' C2/C3 and C6/C7 '''
| width="125" align="center" | ''' '''
| width="125" align="center" | ''' 298.15 K'''
| width="125" align="center" | ''' C2/C3 and C6/C7 '''
| width="125" align="center" | '''298.15 K'''
| width="125" align="center" | ''' 0 K'''
|-
| '''C-C'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''C-C'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

= References =

<references/>